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Korolyuk, Volodymyr Semenovych

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Author ID: korolyuk.vladimir-semenovich Recent zbMATH articles by "Korolyuk, Volodymyr Semenovych"
Published as: Korolyuk, V. S.; Koroliuk, V. S.; Korolyuk, Vladimir S.; Koroliuk, Volodymyr S.; Koroliuk, Vladimir S.; Korolyuk, V.; Korolyuk, Vladimir Semenovich; Korolyuk, Volodymyr S.; Korolyuk, Volodymyr; Koroljuk, V. S.; Korolyuk, Volodymyr Semenovych; Koroliuk, Vladimir; Korolyuk, Vladimir; Koroliouk, V. S.; Koroljuk, W. S.
Further Spellings: Королюк Володимир Семенович
External Links: MGP · Wikidata · GND · IdRef
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Co-Authors

83 single-authored
52 Borovskikh, Yuri V.
28 Limnios, Nikolaos
23 Turbin, Anatoly F.
16 Swishchuk, Anatoliy
15 Skorokhod, Anatoliĭ Volodymyrovych
13 Mytropol’skyĭ, Yuriĭ Oleksiĭovych
11 Gusak, Dmytro V.
11 Samoilenko, Igor V.
10 Samoĭlenko, Anatoliĭ Mykhaĭlovych
9 Berezans’kyĭ, Yuriĭ Makarovych
8 Portenko, Mykola Ivanovych
7 Korolyuk, Vladimir V.
6 Lukovsky, Ivan Oleksandrovych
6 Mishura, Yuliya Stepanivna
6 Perestyuk, Mykola Oleksiĭovych
5 Gnedenko, Boris Vladimirovich
5 Kozachenko, Yuriĭ Vasyl’ovych
5 Lykova, Olga B.
5 Sharkovs’kyĭ, Oleksandr Mykolaĭovych
5 Tomusyak, A. A.
4 Bogolyubov, Nikolaĭ Nikolaevich
4 Boĭchuk, Oleksandr Andriĭovych
4 Ežhov, Igor Ivanovich
4 Makarov, Volodymyr Leonidovych
4 Shurenkov, V. M.
4 Tkachenko, Eh. P.
4 Yadrenko, Mykhaĭlo Ĭosypovych
4 Yurchenko, I. V.
3 Bratijchuk, N. S.
3 D’Amico, Guglielmo
3 Eĭdel’man, Samuïl Davydovych
3 Gorbachuk, Myroslav L’vovych
3 Kartashov, Mykola Valentynovych
3 Kovalenko, Igor Mykolaĭovych
3 Manca, Raimondo
3 Melikov, Agassi Z.
3 Melyaeva, O.
3 Nikitin, A. H.
3 Penev, I. P.
3 Pletnev, A. I.
3 Ponomarenko, Leonid A.
3 Rustamov, A. M.
3 Sakhno, Lyudmyla Mykhaĭlivna
3 Shiryaev, Al’bert Nikolaevich
3 Syta, Halyna M.
3 Velikii, A. P.
3 Yushchenko, E. L.
2 Brodi, S. M.
2 Danilyuk, Ivan Il’ich
2 Demenin, A. N.
2 Drozd, Yuriĭ Anatoliĭovych
2 Erugin, Nikolaĭ Pavlovich
2 Gaĭshun, Ivan Vasil’vich
2 Glushkov, Viktor Mikhaĭlovich
2 Gorodnii, M. F.
2 Il’in, Vladimir Aleksandrovich
2 Izobov, Nikolaĭ Alekseevich
2 Korneĭchuk, Nikolaĭ Pavlovich
2 Koroliouk, Dmytro Volodymyrovych
2 Koshlyakov, Vladimir Nikolaevich
2 Lebedintseva, E. P.
2 Medvedev, Yuriĭ Ivanovich
2 Mikhalevich, Vladimir Semenovich
2 Moklyachuk, Mykhaĭlo Pavlovych
2 Parasyuk, Igor O.
2 Parasyuk, Ostap Stepanovich
2 Pirliev, B.
2 Prokhorov, Yuriĭ Vasil’evich
2 Sachkov, Vladimir Nikolaevich
2 Samoĭlenko, Yuriĭ Stefanovych
2 Sergienko, Ivan Vasylyovych
2 Sharko, Volodymyr Vasil’ovych
2 Shevchenko, Georgiy M.
2 Skrypnik, Igor Vladimirovich
2 Statland, Eh. S.
2 Yasinskij, V. K.
2 Yasynsky, V. K.
1 Albeverio, Sergio A.
1 Alchekov, A. K.
1 Antonyuk, Oleksandra Viktorivna
1 Antonyuk, Svitlana V.
1 Bagro, G. S.
1 Balakrishnan, Narayanaswamy
1 Belousova, S. V.
1 Bertotti, Maria Letizia
1 Bogolyubov, Alekseĭ Nikolaevich
1 Borovkov, Aleksandr Alekseevich
1 Borysenko, Oleksandr Danylovych
1 Buldygin, Valeriĭ Volodymyrovych
1 Butko, T. K.
1 Carkovs, Jevgenijs
1 Chabaniuk, Yaroslav
1 Chabanyuk, Yaroslav M.
1 Cherenkov, A. P.
1 Chetouani, H.
1 Derzko, Nicolas A.
1 Diesperova, M. M.
1 Dobrovol’skij, V. V.
1 Dorohovtsev, A. A.
1 Dovgyĭ, S. O.
...and 79 more Co-Authors
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Serials

43 Ukraïns’kyĭ Matematychnyĭ Zhurnal
31 Ukrainian Mathematical Journal
17 Theory of Probability and its Applications
14 Cybernetics and Systems Analysis
13 Doklady Akademii Nauk Ukrainskoĭ SSR, Seriya A
12 Theory of Probability and Mathematical Statistics
11 Teoriya Ĭmovirnosteĭ ta Matematychna Statystyka
9 Dopovidi Akademiï Nauk Ukraïns’koï RSR. Seriya A
8 Teoriya Veroyatnosteĭ i eë Primeneniya
8 Kibernetika
8 Theory of Stochastic Processes
6 Selected Translations in Mathematical Statistics and Probability
6 Soviet Mathematics. Doklady
5 Journal of Mathematical Sciences (New York)
4 Russian Mathematical Surveys
4 Uspekhi Matematicheskikh Nauk [N. S.]
4 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky
4 Dopovidi Akademiï Nauk Ukraïns’koï RSR
4 Mathematics and its Applications (Dordrecht)
3 Cybernetics
3 Visnyk. Matematyka. Mekhanika. Kyïvs’kyĭ Universytet Imeni Tarasa Shevchenka
2 Computers & Mathematics with Applications
2 Doklady Akademii Nauk SSSR
2 Differentsial’nye Uravneniya
2 Journal of Soviet Mathematics
2 Communications in Statistics. Theory and Methods
2 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
2 Methodology and Computing in Applied Probability
2 Differential Equations
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Stochastics
2 Doklady Akademii Nauk SSSR. Novaya Seriya
1 Izvestiya Akademii Nauk UzSSR. Seriya Fiziko-Matematicheskikh Nauk
1 Stochastic Analysis and Applications
1 Acta Applicandae Mathematicae
1 Soviet Journal of Computer and Systems Sciences
1 Applied Mathematics Letters
1 The Annals of Applied Probability
1 Soviet Physics. Doklady
1 Stochastic Processes and their Applications
1 Stochastics and Stochastics Reports
1 Dopovidi Akademiï Nauk Ukraïni
1 Random Operators and Stochastic Equations
1 Buletinul Academiei de Științe a Republicii Moldova. Matematica
1 Matematychni Metody ta Fizyko-Mekhanichni Polya
1 Proceedings of A. Razmadze Mathematical Institute
1 Applied Stochastic Models in Business and Industry
1 Nonlinear Oscillations
1 Problemy Kibernetiki
1 Springer Optimization and Its Applications

Publications by Year

Citations contained in zbMATH Open

150 Publications have been cited 802 times in 525 Documents Cited by Year
Semi-Markov processes and their applications. (Polumarkovskie processy i ih prilozenija.). Zbl 0371.60106
Korolyuk, V. S.; Turbin, A. F.
67
1976
Stochastic models of systems. Zbl 0960.60004
Korolyuk, V. S.; Korolyuk, V. V.
59
1999
Stochastic systems in merging phase space. Zbl 1101.60003
Koroliuk, Vladimir S.; Limnios, Nikolaos
54
2005
A manual on probability theory and mathematical statistics. (Spravochnik po teorii veroyatnostej i matematicheskoj statistike). 2nd ed., rev. and compl. Zbl 0608.60001
Korolyuk, V. S.; Portenko, N. I.; Skorokhod, A. V.; Turbin, A. F.
50
1985
Mathematical principles for phase extension of complex systems. (Matematiceskie osnovy fazovogo ukrupnenija sloznyh sistem.). Zbl 0411.60003
Korolyuk, V. S.; Turbin, A. F.
45
1978
Markov renewal processes in problems of systems reliability. (Protsessy markovskogo vosstanovleniya v zadachakh nadezhnosti sistem). Zbl 0508.60073
Korolyuk, V. S.; Turbin, A. F.
37
1982
Theory of \(U\)-statistics. Updated and transl. from the Russian by P. V. Malyshev and D. V. Malyshev. Zbl 0785.60015
Korolyuk, V. S.; Borovskikh, Yu. V.
21
1994
On ruin problems for a compound Poisson process. Zbl 0372.60069
Korolyuk, V. S.
20
1975
Diffusion approximation with equilibrium for evolutionary systems switched by semi-Markov processes. Zbl 1093.60057
Korolyuk, V. S.; Limnios, N.
19
2005
On the maximum discrepancy between two empirical distributions. (Über die maximale Divergenz zweier empirischer Verteilungen.) Zbl 0044.13602
Gnedenko, B. V.; Korolyuk, V. S.
18
1951
Stochastic models of systems. (Stokhasticheskie modeli sistem.) Zbl 0753.60083
Korolyuk, V. S.
15
1989
Semi-Markov random evolutions. Transl. from the Russian by V. Zayatas. Zbl 0813.60083
Korolyuk, V. S.; Swishchuk, A. V.
15
1994
Asymptotic analysis of distributions in statistics (Asimptoticheskij analiz raspredelenij statistik). Zbl 0565.62003
Korolyuk, V. S.; Borovskikh, Yu. V.
12
1984
Martingale approximation. Zbl 0912.60063
Borovskikh, Yu. V.; Korolyuk, V. S.
11
1997
On the stability of an autonomous dynamical system with fast Markov switchings. Zbl 0757.60051
Korolyuk, V. S.
10
1991
Methods for analysis of multi-channel queueing system with instantaneous and delayed feedbacks. Zbl 1338.90132
Koroliuk, V. S.; Melikov, A. Z.; Ponomarenko, L. A.; Rustamov, A. M.
10
2016
Semi-Markov processes and their applications. Zbl 0338.60061
Korolyuk, V. S.; Brodi, S. M.; Turbin, A. F.
9
1976
The theory of \(U\)-statistics. (Teoriya \(U\)-statistik.) Zbl 0744.60024
Korolyuk, V. S.; Borovskikh, Yu. V.
8
1989
Method of potential in boundary problems for processes with independent increases and jumps of the same sign. Zbl 0368.60086
Korolyuk, V. S.; Suprun, B. I.; Shurenkov, V. M.
8
1976
On the first passage time across a given level for processes with independent increments. Zbl 0177.21304
Gusak, D. V.; Korolyuk, V. S.
7
1968
Über das asymptotische Verhalten der Zustandszeit eines halb- Markovschen Prozesses in der Untermenge der Zustände. Zbl 0185.46203
Korolyuk, V. S.
7
1969
Diffusion approximation of stochastic Markov models with persistent regression. Zbl 0945.60028
Korolyuk, V. S.; Korolyuk, D. V.
7
1995
Mathematical foundations of the state lumping of large systems. Transl. from the Russ. and upd. by V. V. Zayats and Y. A. Atanov. Zbl 0834.60001
Korolyuk, Vladimir S.; Turbin, Anatoly F.
7
1993
Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach. (Approximations de Lévy et de Poisson des systèmes stochastiques modulés, via une approche basée sur les semi-martingales.) Zbl 1339.60028
Koroliuk, Volodymyr S.; Limnios, Nikolaos; Samoilenko, Igor V.
7
2016
Diffusion approximation of evolutionary systems with equilibrium in asymptotic split phase space. Zbl 1075.60099
Korolyuk, Vladimir S.; Limnios, Nicolaos
6
2005
On the maximum discrepancy between two empirical distributions. Zbl 0112.11006
Gnedenko, B. V.; Korolyuk, V. S.
6
1961
Stability of stochastic systems in the diffusion-approximation scheme. Zbl 0934.93069
Korolyuk, V. S.
6
1998
Problem of large deviations for Markov random evolutions with independent increments in the scheme of asymptotically small diffusion. Zbl 1224.60225
Korolyuk, V. S.
6
2010
Poisson approximation of increment processes with Markov switching. Zbl 1090.60073
Korolyuk, V. S.; Limnios, N.
6
2005
Asymptotic analysis of the system with server vacation and perishable inventory. Zbl 1383.93010
Koroliuk, V. S.; Melikov, A. Z.; Ponomarenko, L. A.; Rustamov, A. M.
6
2017
Central limit theorem for homogeneous processes with independent increments and semi-Markov commutations. Zbl 0539.60089
Korolyuk, V. S.; Korolyuk, V. V.
5
1983
Analytic problems of the asymptotic behavior of probability distributions. (Analiticheskie problemy asimptotiki veroyatnostnykh raspredelenij). Zbl 0541.60017
Korolyuk, V. S.; Borovskikh, Yu. V.
5
1981
Central limit theorem for semi-Markov random evolutions. Zbl 0609.60035
Korolyuk, V. S.; Svishchuk, A. V.
5
1986
On the joint distribution of a process with stationary increments and its maximum. Zbl 0281.60032
Gusak, D. V.; Korolyuk, V. S.
5
1970
Equilibrium processes in biomedical data analysis: the Wright-Fisher model. Zbl 1323.93008
Koroliouk, D. V.; Koroliuk, V. S.; Rosato, N.
5
2014
Random permanents and symmetric statistics. Zbl 0817.60032
Korolyuk, V. S.; Borovskikh, Yu. V.
5
1992
The asymptotic behaviour of semi-Markov processes with a decomposable set of states. Zbl 0234.60105
Gusak, D. V.; Korolyuk, V. S.
5
1971
Asymptotic theory of U-statistics. Zbl 0663.62059
Korolyuk, V. S.; Borovskikh, Yu. V.
4
1988
Convergence rate for degenerate von Mises functionals. Zbl 0668.60037
Korolyuk, V. S.; Borovskikh, Yu. V.
4
1988
Average and diffusion approximation of stochastic evolutionary systems in an asymptotic split state space. Zbl 1041.60061
Korolyuk, Vladimir S.; Limnios, Nikolaos
4
2004
Die Verweilzeit eines semi-Markovschen Prozesses in einer fixierten Menge von Zuständen. Zbl 0135.19003
Korolyuk, V. S.
4
1965
Semi-Markovian processes and their application. Zbl 0183.23403
Ezhov, I. I.; Korolyuk, V. S.
4
1967
Asymptotic expansion of semi-Markov random evolutions. Zbl 1179.60058
Albeverio, S.; Koroliuk, V. S.; Samoilenko, I. V.
4
2009
Poisson approximation of impulsive recurrent process with semi-Markov switching. Zbl 1236.60086
Koroliuk, V. S.; Limnios, N.; Samoilenko, I. V.
4
2011
Markov random evolutions with independent increments in the asymptotically small diffusion scheme. Zbl 1224.60039
Korolyuk, V. S.
4
2010
Poisson approximation of processes with locally independent increments with Markov switching. Zbl 1224.60195
Koroliuk, V. S.; Limnios, N.; Samoilenko, I. V.
4
2009
Queuing systems with semi-Markov flow in average and diffusion approximation schemes. Zbl 1175.60081
Koroliuk, V. S.; Koroliuk, V. V.; Limnios, N.
4
2009
Asymptotic expansion for the distribution of absorption time of a weakly nonhomogeneous Markov chain. Zbl 0478.60079
Korolyuk, V. S.; Penev, I. P.; Turbin, A. F.
4
1981
Stability of an autonomous dynamical system with rapid Markov switchings. Zbl 0725.34054
Korolyuk, V. S.
4
1990
Models of perishable queueing-inventory systems with server vacations. Zbl 1385.93008
Koroliuk, V. S.; Melikov, A. Z.; Ponomarenko, L. A.; Rustamov, A. M.
4
2018
A central limit theorem for U-statistics in a Hilbert space. Zbl 0619.60006
Korolyuk, V. S.; Borovskikh, Yu. V.
3
1987
Über eine Methode zum Beweis von Grenzwertsätzen für gewisse Funktionale von semi-Markovschen Prozessen. Zbl 0246.60063
Korolyuk, V. S.; Turbin, A. F.
3
1972
Increment processes and its stochastic exponential with Markov switching in Poisson approximation scheme. Zbl 1045.60097
Korolyuk, V. S.; Limnios, N.
3
2003
Diffusion approximation for integral functionals in the double merging and averaging scheme. Zbl 0955.60041
Korolyuk, V. S.; Limnios, N.
3
1999
Evolutionary systems in an asymptotic split phase space. Zbl 0965.60086
Korolyuk, Vladimir S.; Limnios, Nikolaos
3
2000
On the results of asymptotic analysis in problems with boundaries. Zbl 0144.18608
Borovkov, A. A.; Korolyuk, V. S.
3
1965
Random permanents. Zbl 0845.60020
Borovskikh, Yu. V.; Korolyuk, V. S.
3
1994
Boundary problems for a compound Poisson process. Zbl 0322.60070
Korolyuk, V. S.
3
1974
Fluctuation of stochastic systems with average equilibrium point. Zbl 1141.60015
Chabaniuk, Yaroslav; Koroliuk, Vladimir S.; Limnios, Nikolaos
3
2007
Superposition of Markov renewal processes. Zbl 0485.60086
Korolyuk, V. S.
3
1981
Random evolutions with locally independent increments on increasing time intervals. Zbl 1291.60155
Korolyuk, Vladimir Semenovich
3
2011
Asymptotische Entwicklungen für die Verträglichkeitskriterien von A. N. Kolmogorov and N. V. Smirnov. Zbl 0056.12904
Korolyuk, V. S.
3
1954
Semi-Markov random evolutions-phase aggregation and applications. Zbl 0900.60077
Koroljuk, V. S.; Swishchuk, A. V.
2
1988
Behavior of the second moment of the solution to the autonomous stochastic linear partial differential equation with random parameters in the right-hand side. Zbl 1327.60130
Koroliuk, V. S.; Yurchenko, I. V.; Yasynskyy, V. K.
2
2015
Large deviation problems for Markov random evolution with independent increments in the scheme of asymptotically small diffusion. Zbl 1315.60036
Koroliuk, Volodymyr S.
2
2011
Random walk on a semi-axis on a superposition of two renewal processes. Zbl 0549.60063
Korolyuk, V. S.; Pirliev, B.
2
1984
Characteristic functions, estimates of moments of U-statistics, and von Mises functionals. Zbl 0565.60019
Korolyuk, V. S.; Borovskikh, Yu. V.
2
1984
Stationary distribution for repairable systems. Zbl 0978.60102
Chetouani, H.; Korolyuk, V. S.
2
2000
Weak convergence of U-statistics to multiple stochastic integrals in Hilbert spaces. Zbl 0621.60007
Korolyuk, V. S.; Borovskikh, Yu. V.
2
1987
Diffusion approximation of integral functionals in merging and averaging scheme. Zbl 0958.60038
Korolyuk, V. S.; Limnios, N.
2
1998
On a hypothesis proposed by B. V. Gnedenko. Zbl 0106.34101
Zolotarev, V. M.; Korolyuk, V. S.
2
1962
On a method of programming. Zbl 0119.33701
Korolyuk, V. S.
2
1958
Random permanents and symmetric statistics. Zbl 0813.60025
Borovskikh, Yuri V.; Korolyuk, Vladimir S.
2
1994
Beschreibung reservierter Systeme mittels semi-Markovscher Prozesse. Zbl 0156.18604
Korolyuk, V. S.; Tomusyak, A. A.
2
1965
On the first passage time of a given level for processes with independent increments. Zbl 0165.19303
Gusak, D. V.; Korolyuk, V. S.
2
1968
On the joint distribution of a process with stationary increments and its maximum. Zbl 0199.52502
Gusak, D. V.; Korolyuk, V. S.
2
1969
Yurij L’vovich Daletskyj (to his 70th birthday). Zbl 0936.01022
Berezanskyj, Yu. M.; Korolyuk, V. S.; Krein, S. G.; Mitropolskij, Yu. A.; Samoilenko, A. M.; Skorokhod, A. V.; Skrypnik, I. V.
2
1997
Perturbation of operators on the spectrum and asymptotical enlargement of Markov chains. Zbl 0319.60043
Korolyuk, V. S.; Turbin, A. F.
2
1975
Asymptotic enlarging of semi-Markov processes with an arbitrary state space. Zbl 0386.60064
Korolyuk, V. S.; Turbin, A. F.
2
1976
Semi-Markov models of complex stochastic systems. Zbl 0411.60090
Korolyuk, Vladimir Semenovich
2
1977
Handbook on probability theory and mathematical statistics. (Spravocnik po teorii verojatnostei i matematiceskoi statistike.). Zbl 0412.60001
2
1978
Queuing system evolution in phase merging scheme. Zbl 1167.60360
Korolyk, V.; Mishkoy, Gh.; Mamonova, A.; Griza, Iu.
2
2008
Stationary phase extension of Markov renewal processes. Zbl 0445.60071
Arias, E.; Korolyuk, V. S.
2
1980
Limit theorems for Markov random evolutions in the scheme of asymptotic state lumping. Zbl 0529.60065
Korolyuk, V. S.; Turbin, A. F.
2
1983
The resolvent of a homogeneous process with independent increments killed on a halfaxis. Zbl 0575.60070
Bratijchuk, N. S.; Korolyuk, V. S.
2
1985
Approximation of nondegenerate U-statistics. Zbl 0593.62009
Korolyuk, V. S.; Borovskikh, Yu. V.
2
1986
Expansions for U-statistics and von Mises functionals. Zbl 0605.62009
Korolyuk, V. S.; Borovskikh, Yu. V.
2
1985
The central limit theorem for additive functionals of Markov and semi- Markov processes. Zbl 0673.60020
Korolyuk, V. S.
2
1986
Phase averaging of inhomogeneous semi-Markov random evolutions. Zbl 0678.60085
Korolyuk, V. S.; Svishchuk, A. V.
2
1989
Stability of dynamic systems with aftereffect under Markov perturbations. Zbl 1153.34352
Korolyuk, V. S.; Musurivskii, V. I.; Yurchenko, I. V.
2
2007
Stochastic models of systems in reliability problems. Zbl 0936.60081
Korolyuk, Vladimir S.
2
1998
Evolution stochastic systems. Averaging algorithms and diffusion approximation. (Evolyutsionnye stokhasticheskie sistemy. Algoritmy usredneniya i diffuzionnoj approksimatsii.) Zbl 0968.60004
Korolyuk, V. S.; Svishchuk, A. V.
2
2000
Approximation of non-degenerate U-statistics. Zbl 0572.62022
Korolyuk, V. S.; Borovskikh, Yu. V.
2
1985
Stability of a dynamical system with semi-Markov switchings under conditions of stability of the averaged system. Zbl 1006.60090
Korolyuk, V. S.; Chabanyuk, Ya. M.
2
2002
Lévy approximation of impulsive recurrent process with semi-Markov switching. Zbl 1249.60171
Koroliuk, V. S.; Limnios, N.; Samoilenko, I. V.
1
2010
Evolution of systems in a semi-Markov random environment. Zbl 0651.60089
Korolyuk, V. S.
1
1987
Random walk on the semiaxis at the superposition of two renewal processes. Zbl 0559.60059
Korolyuk, V. S.; Pirliev, B.
1
1984
Compound Poisson approximation with drift for stochastic additive functionals with Markov and semi-Markov switching. Zbl 1069.60033
Korolyuk, Vladimir S.; Limnios, Nikolaos
1
2005
Anatolij Vladimirovich Skorokhod (on his 70th birthday). Zbl 0972.01038
Kovalenko, I. M.; Korolyuk, V. S.; Portenko, M. I.; Samojlenko, A. M.; Syta, G. M.; Yadrenko, M. I.
1
2000
Limit expression for the U-statistics by a multiple Wiener-Ito integral. Zbl 0619.60026
Korolyuk, V. S.; Borovskikh, Yu. V.
1
1987
Models of perishable queueing-inventory systems with server vacations. Zbl 1385.93008
Koroliuk, V. S.; Melikov, A. Z.; Ponomarenko, L. A.; Rustamov, A. M.
4
2018
Filtration of stationary Gaussian statistical experiments. Zbl 1445.39016
Koroliouk, Dmytro Volodymyrovych; Korolyuk, Volodymyr Semenovych
1
2018
Asymptotic analysis of the system with server vacation and perishable inventory. Zbl 1383.93010
Koroliuk, V. S.; Melikov, A. Z.; Ponomarenko, L. A.; Rustamov, A. M.
6
2017
Methods for analysis of multi-channel queueing system with instantaneous and delayed feedbacks. Zbl 1338.90132
Koroliuk, V. S.; Melikov, A. Z.; Ponomarenko, L. A.; Rustamov, A. M.
10
2016
Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach. (Approximations de Lévy et de Poisson des systèmes stochastiques modulés, via une approche basée sur les semi-martingales.) Zbl 1339.60028
Koroliuk, Volodymyr S.; Limnios, Nikolaos; Samoilenko, Igor V.
7
2016
Stochastic behavioral models. Classification. Zbl 1354.93143
Koroliouk, Dmitri V.; Bertotti, Maria Letizia; Koroliuk, V. S.
1
2016
Behavior of the second moment of the solution to the autonomous stochastic linear partial differential equation with random parameters in the right-hand side. Zbl 1327.60130
Koroliuk, V. S.; Yurchenko, I. V.; Yasynskyy, V. K.
2
2015
B. V. Gnedenko: classic of limit theorems in the theory of probability. Zbl 1311.01022
Koroliuk, Volodymyr S.
1
2015
Equilibrium processes in biomedical data analysis: the Wright-Fisher model. Zbl 1323.93008
Koroliouk, D. V.; Koroliuk, V. S.; Rosato, N.
5
2014
Storage impulsive processes in the merging phase space. Zbl 1304.60054
Koroliuk, Vladimir S.; Manca, Raimondo; D’Amico, Guglielmo
1
2014
Anatolii Mykhailovych Samoilenko (on his 75th birthday). Zbl 1275.01007
Berezans’kyi, Yu. M.; Boichuk, O. A.; Horbachuk, M. L.; Drozd, Yu. A.; Korolyuk, V. S.; Lukovs’kyi, I. O.; Makarov, V. L.; Nikitin, A. H.; Perestyuk, M. O.; Portenko, M. I.; Samoilenko, Yu. S.; Trokhymchuk, Yu. Yu.; Sharko, V. V.; Sharkovs’kyi, O. M.
1
2013
Dynamic random evolutions on increasing time intervals. Zbl 1287.60092
Koroliuk, V. S.
1
2012
Poisson approximation of impulsive recurrent process with semi-Markov switching. Zbl 1236.60086
Koroliuk, V. S.; Limnios, N.; Samoilenko, I. V.
4
2011
Random evolutions with locally independent increments on increasing time intervals. Zbl 1291.60155
Korolyuk, Vladimir Semenovich
3
2011
Large deviation problems for Markov random evolution with independent increments in the scheme of asymptotically small diffusion. Zbl 1315.60036
Koroliuk, Volodymyr S.
2
2011
Problem of large deviations for Markov random evolutions with independent increments in the scheme of asymptotically small diffusion. Zbl 1224.60225
Korolyuk, V. S.
6
2010
Markov random evolutions with independent increments in the asymptotically small diffusion scheme. Zbl 1224.60039
Korolyuk, V. S.
4
2010
Lévy approximation of impulsive recurrent process with semi-Markov switching. Zbl 1249.60171
Koroliuk, V. S.; Limnios, N.; Samoilenko, I. V.
1
2010
Occupation measure functionals in merging phase space. Zbl 1200.60075
Koroliuk, V. S.; Kutoviy, O.; Limnios, N.
1
2010
Asymptotic expansion of semi-Markov random evolutions. Zbl 1179.60058
Albeverio, S.; Koroliuk, V. S.; Samoilenko, I. V.
4
2009
Poisson approximation of processes with locally independent increments with Markov switching. Zbl 1224.60195
Koroliuk, V. S.; Limnios, N.; Samoilenko, I. V.
4
2009
Queuing systems with semi-Markov flow in average and diffusion approximation schemes. Zbl 1175.60081
Koroliuk, V. S.; Koroliuk, V. V.; Limnios, N.
4
2009
Queuing system evolution in phase merging scheme. Zbl 1167.60360
Korolyk, V.; Mishkoy, Gh.; Mamonova, A.; Griza, Iu.
2
2008
First integrals in the diffusion approximation scheme. Zbl 1153.60369
Koroliuk, V. S.; Limnios, N.
1
2008
Fluctuation of stochastic systems with average equilibrium point. Zbl 1141.60015
Chabaniuk, Yaroslav; Koroliuk, Vladimir S.; Limnios, Nikolaos
3
2007
Stability of dynamic systems with aftereffect under Markov perturbations. Zbl 1153.34352
Korolyuk, V. S.; Musurivskii, V. I.; Yurchenko, I. V.
2
2007
Stochastic systems in merging phase space. Zbl 1101.60003
Koroliuk, Vladimir S.; Limnios, Nikolaos
54
2005
Diffusion approximation with equilibrium for evolutionary systems switched by semi-Markov processes. Zbl 1093.60057
Korolyuk, V. S.; Limnios, N.
19
2005
Diffusion approximation of evolutionary systems with equilibrium in asymptotic split phase space. Zbl 1075.60099
Korolyuk, Vladimir S.; Limnios, Nicolaos
6
2005
Poisson approximation of increment processes with Markov switching. Zbl 1090.60073
Korolyuk, V. S.; Limnios, N.
6
2005
Compound Poisson approximation with drift for stochastic additive functionals with Markov and semi-Markov switching. Zbl 1069.60033
Korolyuk, Vladimir S.; Limnios, Nikolaos
1
2005
Stochastic systems with averaging in the scheme of diffusion approximation. Zbl 1093.60056
Korolyuk, V. S.
1
2005
Average and diffusion approximation of stochastic evolutionary systems in an asymptotic split state space. Zbl 1041.60061
Korolyuk, Vladimir S.; Limnios, Nikolaos
4
2004
Lévy approximation of increment processes with Markov switching. Zbl 1063.60044
Korolyuk, Vladimir S.; Limnios, Nikolaos
1
2004
Increment processes and its stochastic exponential with Markov switching in Poisson approximation scheme. Zbl 1045.60097
Korolyuk, V. S.; Limnios, N.
3
2003
Stability of a dynamical system with semi-Markov switchings under conditions of stability of the averaged system. Zbl 1006.60090
Korolyuk, V. S.; Chabanyuk, Ya. M.
2
2002
Poisson approximation of homogeneous additive stochastic functionals with semi-Markov switchings. Zbl 0998.60028
Korolyuk, V. S.; Limnios, N.
1
2001
Evolutionary systems in an asymptotic split phase space. Zbl 0965.60086
Korolyuk, Vladimir S.; Limnios, Nikolaos
3
2000
Stationary distribution for repairable systems. Zbl 0978.60102
Chetouani, H.; Korolyuk, V. S.
2
2000
Evolution stochastic systems. Averaging algorithms and diffusion approximation. (Evolyutsionnye stokhasticheskie sistemy. Algoritmy usredneniya i diffuzionnoj approksimatsii.) Zbl 0968.60004
Korolyuk, V. S.; Svishchuk, A. V.
2
2000
Anatolij Vladimirovich Skorokhod (on his 70th birthday). Zbl 0972.01038
Kovalenko, I. M.; Korolyuk, V. S.; Portenko, M. I.; Samojlenko, A. M.; Syta, G. M.; Yadrenko, M. I.
1
2000
Skorokhod’s ideas in probability theory. Zbl 0956.00022
1
2000
Stochastic models of systems. Zbl 0960.60004
Korolyuk, V. S.; Korolyuk, V. V.
59
1999
Diffusion approximation for integral functionals in the double merging and averaging scheme. Zbl 0955.60041
Korolyuk, V. S.; Limnios, N.
3
1999
Stability of stochastic systems in the diffusion-approximation scheme. Zbl 0934.93069
Korolyuk, V. S.
6
1998
Diffusion approximation of integral functionals in merging and averaging scheme. Zbl 0958.60038
Korolyuk, V. S.; Limnios, N.
2
1998
Stochastic models of systems in reliability problems. Zbl 0936.60081
Korolyuk, Vladimir S.
2
1998
A singular perturbation approach for Liptser’s functional limit theorem and some extensions. Zbl 0941.60089
Korolyuk, V. S.; Limnios, N.
1
1998
Boundary layer in asymptotic analysis for random walks. Zbl 0942.60025
Korolyuk, Vladimir S.
1
1998
Martingale approximation. Zbl 0912.60063
Borovskikh, Yu. V.; Korolyuk, V. S.
11
1997
Yurij L’vovich Daletskyj (to his 70th birthday). Zbl 0936.01022
Berezanskyj, Yu. M.; Korolyuk, V. S.; Krein, S. G.; Mitropolskij, Yu. A.; Samoilenko, A. M.; Skorokhod, A. V.; Skrypnik, I. V.
2
1997
Random permanents of mixed sample matrices. Zbl 0948.60016
Kaneva, E. Yu.; Korolyuk, V. S.
1
1996
Diffusion approximation of stochastic Markov models with persistent regression. Zbl 0945.60028
Korolyuk, V. S.; Korolyuk, D. V.
7
1995
Average and stability of dynamical systems with rapid stochastic switchings. Zbl 0971.93079
Korolyuk, Vladimir S.
1
1995
Normal approximation of random permanents. Zbl 0941.60047
Korolyuk, V. S.; Borovskikh, Yu. V.
1
1995
Theory of \(U\)-statistics. Updated and transl. from the Russian by P. V. Malyshev and D. V. Malyshev. Zbl 0785.60015
Korolyuk, V. S.; Borovskikh, Yu. V.
21
1994
Semi-Markov random evolutions. Transl. from the Russian by V. Zayatas. Zbl 0813.60083
Korolyuk, V. S.; Swishchuk, A. V.
15
1994
Random permanents. Zbl 0845.60020
Borovskikh, Yu. V.; Korolyuk, V. S.
3
1994
Random permanents and symmetric statistics. Zbl 0813.60025
Borovskikh, Yuri V.; Korolyuk, Vladimir S.
2
1994
Mathematical foundations of the state lumping of large systems. Transl. from the Russ. and upd. by V. V. Zayats and Y. A. Atanov. Zbl 0834.60001
Korolyuk, Vladimir S.; Turbin, Anatoly F.
7
1993
Kravchuk’s stochastic polynomials. Zbl 0890.60002
Korolyuk, V. S.
1
1993
Random permanents and symmetric statistics. Zbl 0817.60032
Korolyuk, V. S.; Borovskikh, Yu. V.
5
1992
Semi-Markov random evolutions. (Polumarkovskie sluchajnye ehvolyutsii.) Zbl 0851.60086
Korolyuk, V. S.; Svishchuk, A. V.
1
1992
On the stability of an autonomous dynamical system with fast Markov switchings. Zbl 0757.60051
Korolyuk, V. S.
10
1991
Stability of an autonomous dynamic system with fast Markov switching. Zbl 0786.60073
Korolyuk, V. S.
1
1991
Stability of an autonomous dynamical system with rapid Markov switchings. Zbl 0725.34054
Korolyuk, V. S.
4
1990
\(U\)-statistics with increasing degrees. Zbl 0738.62055
Korolyuk, V. S.; Borovskikh, Yu. V.
1
1990
Weak convergence of semi-Markov random evolutions in an averaging scheme. Zbl 0747.60025
Korolyuk, V. S.; Svishchuk, A. V.
1
1990
Weak convergence of semi-Markov random evolutions (martingale approach). Zbl 0733.60101
Korolyuk, V. S.; Svishchuk, A. V.
1
1990
The rate of convergence in a central limit theorem for UH-statistics. Zbl 0712.60022
Korolyuk, V. S.; Borovskikh, Yu. V.
1
1990
U-statistics from bootstrap-sample. Zbl 0713.62050
Korolyuk, V. S.; Borovskikh, Yu. V.
1
1990
Rate of convergence in the central limit theorem of the UH-statistics. Zbl 0724.60030
Korolyuk, V. S.; Borovskikh, Yu. V.
1
1990
Stochastic models of systems. (Stokhasticheskie modeli sistem.) Zbl 0753.60083
Korolyuk, V. S.
15
1989
The theory of \(U\)-statistics. (Teoriya \(U\)-statistik.) Zbl 0744.60024
Korolyuk, V. S.; Borovskikh, Yu. V.
8
1989
Phase averaging of inhomogeneous semi-Markov random evolutions. Zbl 0678.60085
Korolyuk, V. S.; Svishchuk, A. V.
2
1989
Limit representation of continuous semi-Markovian random evolutions in a scheme of series. Zbl 0694.60082
Korolyuk, V. S.; Svishchuk, A. V.
1
1989
Asymptotic theory of U-statistics. Zbl 0663.62059
Korolyuk, V. S.; Borovskikh, Yu. V.
4
1988
Convergence rate for degenerate von Mises functionals. Zbl 0668.60037
Korolyuk, V. S.; Borovskikh, Yu. V.
4
1988
Semi-Markov random evolutions-phase aggregation and applications. Zbl 0900.60077
Koroljuk, V. S.; Swishchuk, A. V.
2
1988
Diffusion approximation of a redundant Markov system with repair. Zbl 0748.60075
Korolyuk, V. S.; Vavrikovich, L. V.
1
1988
Rate of convergence for degenerate von-Mises functionals. Zbl 0634.60030
Korolyuk, V. S.; Borovskikh, Yu. V.
1
1988
A central limit theorem for U-statistics in a Hilbert space. Zbl 0619.60006
Korolyuk, V. S.; Borovskikh, Yu. V.
3
1987
Weak convergence of U-statistics to multiple stochastic integrals in Hilbert spaces. Zbl 0621.60007
Korolyuk, V. S.; Borovskikh, Yu. V.
2
1987
Evolution of systems in a semi-Markov random environment. Zbl 0651.60089
Korolyuk, V. S.
1
1987
Limit expression for the U-statistics by a multiple Wiener-Ito integral. Zbl 0619.60026
Korolyuk, V. S.; Borovskikh, Yu. V.
1
1987
A central limit theorem in a scheme of phase extension for semi-Markovian random evolutions. Zbl 0632.60091
Korolyuk, V. S.; Svishchuk, A. V.; Korolyuk, V. V.
1
1987
Central limit theorem for semi-Markov random evolutions. Zbl 0609.60035
Korolyuk, V. S.; Svishchuk, A. V.
5
1986
Approximation of nondegenerate U-statistics. Zbl 0593.62009
Korolyuk, V. S.; Borovskikh, Yu. V.
2
1986
The central limit theorem for additive functionals of Markov and semi- Markov processes. Zbl 0673.60020
Korolyuk, V. S.
2
1986
A manual on probability theory and mathematical statistics. (Spravochnik po teorii veroyatnostej i matematicheskoj statistike). 2nd ed., rev. and compl. Zbl 0608.60001
Korolyuk, V. S.; Portenko, N. I.; Skorokhod, A. V.; Turbin, A. F.
50
1985
The resolvent of a homogeneous process with independent increments killed on a halfaxis. Zbl 0575.60070
Bratijchuk, N. S.; Korolyuk, V. S.
2
1985
Expansions for U-statistics and von Mises functionals. Zbl 0605.62009
Korolyuk, V. S.; Borovskikh, Yu. V.
2
1985
Approximation of non-degenerate U-statistics. Zbl 0572.62022
Korolyuk, V. S.; Borovskikh, Yu. V.
2
1985
Asymptotic analysis of distributions in statistics (Asimptoticheskij analiz raspredelenij statistik). Zbl 0565.62003
Korolyuk, V. S.; Borovskikh, Yu. V.
12
1984
Random walk on a semi-axis on a superposition of two renewal processes. Zbl 0549.60063
Korolyuk, V. S.; Pirliev, B.
2
1984
Characteristic functions, estimates of moments of U-statistics, and von Mises functionals. Zbl 0565.60019
Korolyuk, V. S.; Borovskikh, Yu. V.
2
1984
Random walk on the semiaxis at the superposition of two renewal processes. Zbl 0559.60059
Korolyuk, V. S.; Pirliev, B.
1
1984
Central limit theorem for homogeneous processes with independent increments and semi-Markov commutations. Zbl 0539.60089
Korolyuk, V. S.; Korolyuk, V. V.
5
1983
Limit theorems for Markov random evolutions in the scheme of asymptotic state lumping. Zbl 0529.60065
Korolyuk, V. S.; Turbin, A. F.
2
1983
Functionals on the occupation period of the system M\(| G| 1| \infty\). Zbl 0533.60096
Belousova, S. V.; Korolyuk, V. S.
1
1983
...and 50 more Documents
all top 5

Cited by 498 Authors

52 Korolyuk, Volodymyr Semenovych
19 Limnios, Nikolaos
18 Samoilenko, Igor V.
16 Melikov, Agassi Z.
14 Chabanyuk, Yaroslav M.
13 Swishchuk, Anatoliy
11 Borovskikh, Yuri V.
10 Anisimov, Vladimir Vladislavovič
10 Peschanskij, A. I.
10 Silvestrov, Dmitrii
9 Nikitin, Anatolii V.
9 Nikitin, Yakov Yu.
9 Pogorui, Anatoliy A.
9 Ponomarenko, Leonid A.
9 Yasinskij, V. K.
8 Rodríguez-Dagnino, Ramón Martín
8 Volkova, Ksenia Yu.
7 Bratijchuk, N. S.
7 Manca, Raimondo
7 Obzherin, Yuriy E.
7 Rozenberg, Valerii L’vovich
6 Malyk, Igor V.
6 Shurenkov, V. M.
6 Silvestrov, Sergei D.
6 Yurchenko, I. V.
5 D’Amico, Guglielmo
5 Korolyuk, Vladimir V.
5 Kovalenko, Igor Mykolaĭovych
5 Lukashiv, Taras O.
5 Nakonechnyj, A. N.
5 Rudenko, E. A.
5 Rustamov, A. M.
5 Tsarkov, K. A.
5 Yasynsky, V. K.
4 Boĭchuk, Oleksandr Andriĭovych
4 Cherenkov, A. P.
4 Csáki, Endre
4 Fatalov, Vadim Rolandovich
4 Frolov, S. I.
4 Khimka, U. T.
4 Kolesnik, Alexander D.
4 Kuznetsov, N. Yu.
4 Milošević, Bojana
4 Pirdzhanov, B.
4 Pokutnyĭ, Oleksandr Olekseevich
4 Prabhu, Narahari Umanath
4 Rempała, Grzegorz A.
4 Turbin, Anatoly F.
3 Bouzebda, Salim
3 Chiquet, Julien
3 Engström, Christopher
3 Gusak, Dmytro V.
3 Koroliouk, Dmitri Vladimirovich
3 Kulik, Alexey M.
3 Lebedev, Eugene A.
3 Livinska, Hanna
3 Lukashuk, L. I.
3 Obradović, Marko
3 Rubinovitch, Michael
3 Shpak, Valentyn D.
3 Suprun, V. N.
3 Sztrik, János
3 Tsarkov, Ye. F.
3 Veretennikov, Alexander Yu.
3 Wesołowski, Jacek
3 Yambartsev, Anatoly A.
3 Yarova, O. A.
3 Zhuravlëv, Viktor Filippovich
3 Zitikis, Ričardas
2 Abola, Benard
2 Altman, Eitan
2 Antonyuk, Svitlana V.
2 Avrachenkov, Konstantin Evgen’evich
2 Bentkus, Vidmants-Kastytis
2 Biganda, Pitos Seleka
2 Bogomolov, S. V.
2 Bratiichuk, M. S.
2 Bratiychuk, Mykola S.
2 Cuparić, Marija
2 Dovgyĭ, S. O.
2 Dzhalladova, Irada A.
2 Elejko, Ya. I.
2 Fattakhova, M. I.
2 Grabski, Franciszek
2 Kharlamov, Boris Pavlovich
2 Hössjer, Ola G.
2 Islam, Mohammad Shafiqul
2 Ivaneshkin, A. I.
2 Janssen, Jacques
2 Kakuba, Godwin
2 Kakubava, Revaz
2 Kempa, Wojciech M.
2 Kim, Chesoong
2 Kinash, O. M.
2 Kovalenko, A. I.
2 Kuchment, Peter A.
2 Kukush, Oleksandr Georgiĭovych
2 Kushnir, O. O.
2 Kushnir, V. P.
2 Kuznetsov, I. N.
...and 398 more Authors
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Cited in 117 Serials

83 Cybernetics and Systems Analysis
76 Ukrainian Mathematical Journal
30 Theory of Probability and Mathematical Statistics
29 Journal of Mathematical Sciences (New York)
24 Cybernetics
24 Automation and Remote Control
22 Journal of Soviet Mathematics
11 Statistics & Probability Letters
9 Journal of Statistical Planning and Inference
8 Stochastic Processes and their Applications
7 Mathematical Notes
7 Journal of Computer and Systems Sciences International
7 Methodology and Computing in Applied Probability
6 Applied Mathematics and Computation
5 Annals of the Institute of Statistical Mathematics
5 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
4 Advances in Applied Probability
4 Journal of Statistical Physics
4 Lithuanian Mathematical Journal
4 Problems of Information Transmission
4 Journal of Multivariate Analysis
4 Communications in Statistics. Theory and Methods
4 Random Operators and Stochastic Equations
4 Doklady Mathematics
3 Computers & Mathematics with Applications
3 Journal of Applied Probability
3 Siberian Mathematical Journal
3 Acta Applicandae Mathematicae
3 Probability Theory and Related Fields
3 Journal of Theoretical Probability
3 Proceedings of the Steklov Institute of Mathematics
2 The Annals of Probability
2 The Annals of Statistics
2 Insurance Mathematics & Economics
2 Stochastic Analysis and Applications
2 Asia-Pacific Journal of Operational Research
2 Queueing Systems
2 Annals of Operations Research
2 The Annals of Applied Probability
2 Computational Mathematics and Mathematical Physics
2 Computational Statistics and Data Analysis
2 Vestnik St. Petersburg University. Mathematics
2 Top
2 Matematychni Studiï
2 Econometric Theory
2 Differential Equations
2 Matematicheskoe Modelirovanie
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Nonlinear Oscillations
2 Journal of Theoretical Biology
1 The Canadian Journal of Statistics
1 Journal of Applied Mathematics and Mechanics
1 Metrika
1 Physica A
1 Theoretical and Mathematical Physics
1 Arkiv för Matematik
1 Bulletin of the Polish Academy of Sciences. Technical Sciences
1 Theory of Probability and its Applications
1 Applied Mathematics and Optimization
1 Functional Analysis and its Applications
1 Journal of Combinatorial Theory. Series A
1 Journal of Computational and Applied Mathematics
1 Monatshefte für Mathematik
1 Theoretical Population Biology
1 Tokyo Journal of Mathematics
1 Transactions of the American Mathematical Society
1 European Journal of Combinatorics
1 Operations Research Letters
1 Journal of Time Series Analysis
1 Acta Mathematica Hungarica
1 Applied Mathematics Letters
1 Mathematical and Computer Modelling
1 Discrete Mathematics and Applications
1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique
1 Applied Mathematical Modelling
1 Communications in Statistics. Simulation and Computation
1 European Journal of Operational Research
1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
1 Doklady Akademii Nauk
1 Russian Mathematics
1 Applicationes Mathematicae
1 Mathematical Methods of Statistics
1 Statistical Papers
1 Georgian Mathematical Journal
1 Opuscula Mathematica
1 Electronic Journal of Probability
1 Mathematical Problems in Engineering
1 Functional Differential Equations
1 Mathematical Methods of Operations Research
1 Journal of Inequalities and Applications
1 Journal of Applied Mathematics and Decision Sciences
1 Discrete Dynamics in Nature and Society
1 Statistical Inference for Stochastic Processes
1 International Journal of Applied Mathematics and Computer Science
1 Lobachevskii Journal of Mathematics
1 Brazilian Journal of Probability and Statistics
1 Scandinavian Actuarial Journal
1 Differentsial’nye Uravneniya i Protsessy Upravleniya
1 Journal of Applied Mathematics
1 Stochastic Models
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