Kopytko, Bohdan; Osypchuk, Mykhailo; Shevchuk, Roman Diffusion in media with membranes and some nonlocal parabolic problems. (English) Zbl 07841466 Ukr. Math. J. 75, No. 11, 1641-1665 (2024); and Ukr. Mat. Zh. 75, No. 11, 1450-1472 (2023). MSC: 60J60 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, B. I.; Portenko, M. I. On a multidimensional Brownian motion with a membrane located on a given hyperplane. (English) Zbl 1511.60117 Stochastic Processes Appl. 160, 371-385 (2023). MSC: 60J65 60J60 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, B. I.; Portenko, M. I. Brownian motion in a Euclidean space with a membrane located on a given hyperplane. (Ukrainian. English summary) Zbl 1499.60276 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2022, No. 1, 3-10 (2022). MSC: 60J65 60J60 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, B. I.; Shevchuk, R. V. One-dimensional Wiener process with the properties of partial reflection and delay. (English) Zbl 1483.60113 Carpathian Math. Publ. 13, No. 2, 534-544 (2021). MSC: 60J60 35K20 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, B. I.; Novosyadlo, A. F. On a nonclassical problem for the heat equation and the Feller semigroup generated by it. (English) Zbl 1454.60123 Carpathian Math. Publ. 12, No. 2, 297-310 (2020). MSC: 60J60 35K20 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, Bohdan; Shevchuk, Roman One-dimensional diffusion processes with moving membrane: partial reflection in combination with jump-like exit of process from membrane. (English) Zbl 1441.60061 Electron. J. Probab. 25, Paper No. 41, 21 p. (2020). MSC: 60J60 35K20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Kopytko, B. I.; Shevchuk, R. V. The nonlocal conjugation problem for one-dimensional parabolic equation with discontinuous coefficients and associated Feller semigroup. (English) Zbl 1449.60124 Theory Stoch. Process. 24, No. 2, 17-31 (2019). MSC: 60J60 35K20 60H15 × Cite Format Result Cite Review PDF Full Text: Link
Kopytko, B. I.; Shevchuk, R. V. On Feller semigroup generated by solution of nonlocal parabolic conjugation problem. (English) Zbl 1411.60117 Carpathian Math. Publ. 10, No. 2, 333-345 (2018). MSC: 60J60 35K20 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, Bohdan; Tsapovska, Zhanneta Solution of one initial-boundary Wentzel problem for a parabolic equation with discontinuous coefficients by the boundary integral equation method. (English) Zbl 07328064 J. Appl. Math. Comput. Mech. 16, No. 1, 51-62 (2017). MSC: 35K20 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, Bohdan; Shevchuk, Roman One-dimensional diffusion processes in half-bounded domains with reflection and a possible jump-like exit from a moving boundary. (English) Zbl 1462.60103 J. Appl. Math. Comput. Mech. 15, No. 4, 71-82 (2016). MSC: 60J60 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, Bohdan; Zhernovyi, Kostyantyn Steady-state characteristics of three-channel queueing systems with Erlangian service times. (English) Zbl 1462.90037 J. Appl. Math. Comput. Mech. 15, No. 3, 75-87 (2016). MSC: 90B22 60K25 × Cite Format Result Cite Review PDF Full Text: DOI
Zhernovyi, Yuriy; Kopytko, Bohdan The potentials method for the \(M/G/1/m\) queue with customer dropping and hysteretic strategy of the service time change. (English) Zbl 1462.90043 J. Appl. Math. Comput. Mech. 15, No. 1, 197-210 (2016). MSC: 90B22 60K25 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, B. I.; Shevchuk, R. V. On Feller semigroups associated with one-dimensional diffusion processes with membranes. (English) Zbl 1363.60108 Theory Stoch. Process. 21, No. 1, 31-44 (2016). MSC: 60J60 × Cite Format Result Cite Review PDF
Zhernovyi, Yuriy; Kopytko, Bohdan The potentials method for a closed queueing system with hysteretic strategy of the service time change. (English) Zbl 07251894 J. Appl. Math. Comput. Mech. 14, No. 2, 131-143 (2015). MSC: 60K25 × Cite Format Result Cite Review PDF Full Text: DOI
Zhernovyi, Yuriy; Kopytko, Bohdan; Zhernovyi, Kostyantyn On characteristics of the \(M^{\theta}/G/1/m\) and \(M^{\theta}/G/1\) queues with queue-size based packet dropping. (English) Zbl 1524.60250 J. Appl. Math. Comput. Mech. 13, No. 4, 163-175 (2014). MSC: 60K25 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, Bohdan; Shevchuk, Roman One-dimensional diffusions in bounded domains with a possible jump-like exit from a sticky boundary. (English) Zbl 1524.60177 J. Appl. Math. Comput. Mech. 13, No. 3, 101-114 (2014). MSC: 60J60 60J70 × Cite Format Result Cite Review PDF Full Text: DOI
Zhernovyi, Yuriy; Kopytko, Bohdan The system \(M_{2}^{\theta}/G/1/m\) with threshold control of the arrival rate and service time. (English) Zbl 1524.60249 J. Appl. Math. Comput. Mech. 13, No. 2, 149-163 (2014). MSC: 60K25 93C83 × Cite Format Result Cite Review PDF Full Text: DOI
Zhernovyi, Yuriy; Kopytko, Bohdan The queueing system \(M_{2}^{X}/M/n\) with hysteretic control of the input flow intensity. (English) Zbl 1473.60148 J. Appl. Math. Comput. Mech. 13, No. 1, 149-161 (2014). MSC: 60K25 × Cite Format Result Cite Review PDF Full Text: DOI
Zhernovyi, Yuriy; Kopytko, Bohdan; Zhernovyi, Kostyantyn The busy period for the \(\mathrm{M}^{\theta}/\mathrm{G}/1/m\) system with service time dependent of the queue length. (English) Zbl 1364.60127 J. Appl. Math. Comput. Mech. 12, No. 4, 127-133 (2013). MSC: 60K25 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, Bohdan; Shevchuk, Roman Diffusions in one-dimensional bounded domains with reflection, absorption and jumps at the boundary and at some interior point. (English) Zbl 1364.47006 J. Appl. Math. Comput. Mech. 12, No. 1, 55-68 (2013). MSC: 47D07 31E05 31A25 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, B. I.; Shevchuk, R. V. One-dimensional diffusion processes in bounded domains with boundary conditions and conjugation condition of the Feller-Wentzell type. (Ukrainian. English summary) Zbl 1313.60140 Bukovyn. Mat. Zh. 1, No. 1-2, 77-85 (2013). MSC: 60J60 47D07 × Cite Format Result Cite Review PDF
Kononchuk, P. P.; Kopytko, B. I. Semigroups of operators that describe a Feller process on the line, which is the result of pasting together two diffusion processes. (English. Ukrainian original) Zbl 1290.60073 Theory Probab. Math. Stat. 84, 87-97 (2012); translation from Teor. Jmovirn. Mat. Stat. 84, 84-93 (2011). Reviewer: Ion C. Vladimirescu (Craiova) MSC: 60J45 60J60 47D07 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, B. I.; Shevchuk, R. An inhomogeneous diffusion process model on a half-line with general boundary condition of Feller-Wentzel. (Ukrainian. English, Russian summaries) Zbl 1391.60194 Carpathian Math. Publ. 3, No. 2, 88-99 (2011). MSC: 60J60 × Cite Format Result Cite Review PDF
Zhernovyj, K. Yu.; Kopytko, B. I. The stationary characteristics of \(M^{\theta}/M/1\) and \(M^{\theta}/M/1/m\) systems with two-speed service. (Ukrainian. English summary) Zbl 1249.60193 Nauk. Visn. Chernivets’kogo Univ., Mat. 1, No. 4, 43-51 (2011). MSC: 60K25 × Cite Format Result Cite Review PDF
Kopytko, B. I.; Shevchuk, R. V. On pasting together two inhomogeneous diffusion processes on a line with the general Feller-Wentzell conjugation condition. (English) Zbl 1249.60173 Theory Stoch. Process. 17, No. 2, 55-70 (2011). MSC: 60J60 × Cite Format Result Cite Review PDF
Kopytko, B. I.; Novosyadlo, A. F. An analytic model of generalized diffusion processes with membrane located on a curved surface. (Ukrainian. English summary) Zbl 1240.60221 Nauk. Visn. Chernivets’kogo Univ., Mat. 1, No. 1-2, 64-75 (2011). MSC: 60J60 × Cite Format Result Cite Review PDF
Kopytko, B. I.; Mylyo, O. Ya.; Tsapovska, Zh. Ya. A parabolic conjugation problem with general boundary condition and a conjugation condition of Wentzel type. (Ukrainian. English, Russian summaries) Zbl 1515.35114 Carpathian Math. Publ. 2, No. 2, 55-73 (2010). MSC: 35K20 35A01 35R05 × Cite Format Result Cite Review PDF
Kononchuk, P. P.; Kopytko, B. I. On a diffusion process on a half-line with Feller-Wentzel boundary condition that corresponds to reflection and jumps. (English) Zbl 1249.60172 Theory Stoch. Process. 16, No. 2, 69-76 (2010). MSC: 60J60 × Cite Format Result Cite Review PDF
Kopytko, Bohdan I.; Portenko, Mykola I. The problem of pasting together two diffusion processes and classical potentials. (English) Zbl 1224.60203 Theory Stoch. Process. 15, No. 2, 126-139 (2009). MSC: 60J60 60J35 × Cite Format Result Cite Review PDF
Kopytko, Bohdan I.; Novosyadlo, Andriy F. The Brownian motion process with generalized diffusion matrix and drift vector. (English) Zbl 1224.60202 Theory Stoch. Process. 14, No. 2, 60-70 (2008). MSC: 60J60 × Cite Format Result Cite Review PDF
Kopytko, B. I.; Tsapovs’ka, Zh. Ya. Initial-boundary-value problem with conjugation condition of Wentzel type for a parabolic equation with discontinuous coefficients. (Ukrainian, English) Zbl 1164.35040 Mat. Metody Fiz.-Mekh. Polya 51, No. 1, 7-16 (2008); translation in J. Math. Sci., New York 160, No. 3, 283-295 (2009). Reviewer: V. V. Vlasov (Moskva) MSC: 35K15 × Cite Format Result Cite Review PDF
Kononchuk, Pavlo; Kopytko, Bohdan On the semigroup of Feller operators that describes a diffusion process on the half-line with nonlocal boundary conditions. (Ukrainian. English summary) Zbl 1199.60291 Mat. Visn. Nauk. Tov. Im. Shevchenka 4, 134-143 (2007). MSC: 60J60 × Cite Format Result Cite Review PDF
Kopytko, Bogdan I.; Tsapovs’ka, Zhanneta Ya. A multidimensional model of the diffusion process with membrane whose properties are described by a general Wentzel boundary condition. (English) Zbl 1142.60365 Theory Stoch. Process. 12, No. 28, Part 1-2, 77-86 (2006). MSC: 60H10 × Cite Format Result Cite Review PDF
Kopytko, Bogdan I.; Portenko, Mykola I. An example of a stochastic differential equation with the property of weak non-uniqueness of a solution. (English) Zbl 1142.60386 Theory Stoch. Process. 12, No. 28, Part 1-2, 68-76 (2006). MSC: 60J60 60J35 × Cite Format Result Cite Review PDF
Kopytko, Bogdan I.; Portenko, Mykola I. One more example of a diffusion process whose local characteristics do not determine uniquely its transition probability. (English) Zbl 1142.60385 Theory Stoch. Process. 11, No. 27, Part 1-2, 74-80 (2005). MSC: 60J60 × Cite Format Result Cite Review PDF
Portenko, M. I.; Kopytko, B. I. The example of a diffusion process, whose Kolmogorov local characteristics do not determine uniquely its transition probabilities. (Ukrainian. English summary) Zbl 1088.60084 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2005, No. 5, 26-32 (2005). MSC: 60J60 35K57 35R60 × Cite Format Result Cite Review PDF
Guran, S. I.; Kopytko, B. I. One dimensional diffusion model with partial reflection and delay at a fixed point. (English) Zbl 1065.60109 Mat. Stud. 23, No. 1, 103-107 (2005). MSC: 60J60 × Cite Format Result Cite Review PDF
Kopytko, Bogdan I.; Portenko, Bogdan I. On a multidimensional Brownian motion with a membrane located on a hyperplane and acting in an oblique direction. (English) Zbl 1097.60066 Ukrainian mathematical congress – 2001, Kiev, Ukraine, August 21–23, 2001. Proceedings. Section 9. Probability theory and mathematical statistics. Kyïv: Instytut Matematyky NAN Ukraïny (ISBN 966-02-2616-0). 73-84 (2002). MSC: 60J65 60H10 60J60 × Cite Format Result Cite Review PDF
Yelejko, Ya.; Kopytko, B.; Grishchuk, R. Pricing of bills in transitional period. (Ukrainian. English summary) Zbl 1122.91320 Visn. L’viv. Univ., Ser. Prykl. Mat. Inform. 2002, No. 5, 83-88 (2002). MSC: 91B24 × Cite Format Result Cite Review PDF
Mitropol’skij, Yu. A.; Samoilenko, A. M.; Skorokhod, A. V.; Korolyuk, V. S.; Dorohovtsev, A. A.; Kopytko, B. I.; Syta, H. M. Mykola Ivanovych Portenko (on his 60th birthday). (English. Ukrainian original) Zbl 1002.60500 Ukr. Math. J. 54, No. 2, 177-178 (2002); translation from Ukr. Mat. Zh. 54, No. 2, 147-148 (2002). MSC: 60-03 01A70 × Cite Format Result Cite Review PDF
Kopytko, Bogdan; Tsapovs’ka, Zhanetta The potential method in a parabolic boundary problem with the Ventsel boundary condition. (Ukrainian. English summary) Zbl 0972.35157 Visn. L’viv. Univ., Ser. Mekh.-Mat. 56, 106-115 (2000). MSC: 35Q60 35K20 31A10 × Cite Format Result Cite Review PDF
Kopytko, Bohdan I.; Tsapovska, Zhanneta Ya. Integral representation of an operator semigroup describing a diffusion process in a domain with general Wentzel’s boundary condition. (English) Zbl 0993.60080 Theory Stoch. Process. 5(21), No. 3-4, 105-112 (1999). Reviewer: Mikhail Moklyachuk (Kyïv) MSC: 60J60 58J65 35R60 60H15 × Cite Format Result Cite Review PDF
Kopytko, B. I. An application of the potential method for constructing a diffusion process in a domain with Ventsel boundary condition. (English. Ukrainian original) Zbl 0959.60069 Theory Probab. Math. Stat. 59, 93-100 (1999); translation from Teor. Jmorvirn. Mat. Stat. 59, 91-98 (1998). Reviewer: A.V.Swishchuk (Kyïv) MSC: 60J60 60J50 × Cite Format Result Cite Review PDF
Kopytko, Bogdan I.; Tsapovska, Zhanna J. Diffusion processes with discontinuous local characteristics of the movement. (English) Zbl 0940.60079 Theory Stoch. Process. 4(20), No. 1-2, 139-146 (1998). Reviewer: Yu.V.Kozachenko (Kyïv) MSC: 60H10 60J60 × Cite Format Result Cite Review PDF
Kopytko, B. I. Parabolic equations with discontinuous coefficients and generalized diffusion processes. (Russian) Zbl 1026.60514 Theory Stoch. Process. 1(17), No. 1, 45-55 (1995). Reviewer: A.D.Borisenko (Kyïv) MSC: 60J60 35K15 × Cite Format Result Cite Review PDF
Kopytko, B. I. Construction of the diffusion process with generalized drift vector by means of solution of some conjugation problem for the second-order parabolic type equation. (English) Zbl 0842.60078 Random Oper. Stoch. Equ. 2, No. 2, 189-194 (1994). Reviewer: M.Chaleyat-Maurel (Paris) MSC: 60J60 60H15 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, B. I. Semigroups of operators describing a multi-dimensional diffusion with partially reflecting barrier on a hyperplane. (English) Zbl 0842.60077 Random Oper. Stoch. Equ. 1, No. 1, 95-102 (1993). MSC: 60J60 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, B. I. On existence of the operator semigroup which describes a Wiener process in a semibounded domain with non-classical limit conditions. (Ukrainian) Zbl 0945.60507 Mat. Stud. 2, 94-100 (1993). MSC: 60H15 × Cite Format Result Cite Review PDF
Kopytko, B. I. Diffusion processes with generalized drift vector and diffusion matrix. (English) Zbl 0818.60070 Shiryaev, A. N. (ed.) et al., Probability theory and mathematical statistics. Proceedings of the 6th USSR-Japan symposium, Kiev, USSR, 5-10 August, 1991. Singapore: World Scientific. 169-175 (1992). MSC: 60J60 × Cite Format Result Cite Review PDF
Kopytko, B. I. Connecting two diffusion processes with constant diffusion matrices on a hyperplane. (Über das Verknüpfen zweier Diffusionsprozesse mit konstanten Diffusionsmatrizen auf einer Hyperebene.) (German) Zbl 0745.60081 Stochastic processes and related topics, Proc. Wintersch. Stochastic Processes Optim. Control, Georgenthal/Germ. 1990, Math. Res. 61, 75-79 (1991). Reviewer: P.Kröger (Erlangen) MSC: 60J60 35K20 35K05 × Cite Format Result Cite Review PDF
Kopytko, B. I. Multidimensional diffusion process with partially reflecting screen on hyperplane. (Ukrainian) Zbl 0945.60509 Mat. Stud. 1, 81-88 (1991). MSC: 60J60 × Cite Format Result Cite Review PDF
Kopytko, B. I. Semigroups of operators describing generalized diffusion in a finite- dimensional Euclidean space. (Russian) Zbl 0721.60085 Stochastic analysis and its application, Collect. Sci. Works, Kiev, 70-78 (1989). Reviewer: J.M.Stoyanov (Kingston/Ontario) MSC: 60J60 × Cite Format Result Cite Review PDF
Kopytko, B. I. The generalized diffusion on the plane. (Russian) Zbl 0701.60077 Selected problems of the modern theory of stochastic processes, Collect. Sci. Works, 90-95 (1988). Reviewer: B.Grigelionis MSC: 60J60 60J50 × Cite Format Result Cite Review PDF
Kopytko, B. I. Diffusion processes with the generalized displacement vector concentrated on the hyperplane of discontinuity of the diffusion matrix. (Russian) Zbl 0633.60093 Probabilistic methods for the investigation of systems with an infinite number of degrees of freedom, Collect. sci. Works, Kiev 1986, 65-71 (1986). Reviewer: N.M.Zinchenko MSC: 60J60 60J25 × Cite Format Result Cite Review PDF
Kopytko, B. I. On the glueing of two diffusion processes in a finite-dimensional Euclidean space. (Russian) Zbl 0594.60082 Stochastic processes. Theory and practice, Collect. sci. Works, Kiev 1985, 53-61 (1985). Reviewer: A.Korzeniowski MSC: 60J60 47D07 × Cite Format Result Cite Review PDF
Kopytko, B. I. Gluing two diffusion processes on the plane. (Russian) Zbl 0579.60076 Some questions of the theory of stochastic processes, Collect. sci. Works, Kiev 1984, 48-64 (1984). Reviewer: B.Grigelionis MSC: 60J60 60J50 × Cite Format Result Cite Review PDF
Kopytko, B. I.; Portenko, N. I. Analytical methods of pasting together of diffusion processes. (English) Zbl 0531.60073 Probability theory and mathematical statistics, Proc. 4th USSR-Jap. Symp., Tbilisi/USSR 1982, Lect. Notes Math. 1021, 318-326 (1983). Reviewer: I.Vladimirescu MSC: 60J60 58J65 60H25 60J65 × Cite Format Result Cite Review PDF
Kopytko, B. I. Sewing two nonhomogeneous diffusion processes on a straight line. (English. Russian original) Zbl 0515.60080 Ukr. Math. J. 35, 135-141 (1983); translation from Ukr. Mat. Zh. 35, No. 2, 156-163 (1983). MSC: 60J60 60G20 × Cite Format Result Cite Review PDF Full Text: DOI
Kopytko, B. I.; Portenko, N. I. A remark concerning the processes sewn of two processes of Brownian motion. (Russian) Zbl 0531.60074 Some questions of the theory of stochastic processes, Collect. sci. Work Kiev 1982, 67-79 (1982). Reviewer: L.Podkaminer MSC: 60J65 60H25 × Cite Format Result Cite Review PDF
Kopytko, B. I. Non-homogeneous diffusion processes with a generalized transient coefficient. (Russian) Zbl 0513.60076 Probabilistic infinite dimensional analysis, Collect. sci. Works, Kiev 1981, 59-74 (1981). MSC: 60J60 60G20 60J25 × Cite Format Result Cite Review PDF
Kopytko, B. I. On the sewing of two diffusion processes on the straight line. (Russian) Zbl 0463.60065 Probability methods of infinite-dimensional analysis, Collect. sci. Works, Kiev 1980, 84-101 (1980). MSC: 60J60 × Cite Format Result Cite Review PDF
Kopytko, B. I. On the sewing of two processes of the Brownian motion. (Russian) Zbl 0439.60080 Stochastic processes in problems of mathematical physics, Collect. sci. Works, Kiev 1979, 94-106 (1979). MSC: 60J65 60H10 60J35 × Cite Format Result Cite Review PDF
Balinskij, A. I.; Kopytko, B. I. On conditions concerning the distribution of the roots of a polynomial within the unit circle. (Russian) Zbl 0438.30004 Mat. Metody Fiz.-Mekh. Polya 10, 11-15 (1979). MSC: 30C15 30C10 × Cite Format Result Cite Review PDF