Krasnitskiy, Sergey; Kurchenko, Oleksandr; Syniavska, Olga Limit theorems of Baxter type for generalized random Gaussian processes with independent values. (English) Zbl 1533.60044 Malyarenko, Anatoliy (ed.) et al., Stochastic processes, statistical methods, and engineering mathematics. SPAS 2019, Västerås, Sweden, September 30 – October 2, 2019. Cham: Springer. Springer Proc. Math. Stat. 408, 197-210 (2022). MSC: 60G15 PDFBibTeX XMLCite \textit{S. Krasnitskiy} et al., Springer Proc. Math. Stat. 408, 197--210 (2022; Zbl 1533.60044) Full Text: DOI
Krasnitskiy, S. M.; Kurchenko, O. O. On Baxter type theorems for generalized random Gaussian processes with independent values. (English. Russian original) Zbl 1456.60087 Cybern. Syst. Anal. 56, No. 2, 223-230 (2020); translation from Kibern. Sist. Anal. 2020, No. 2, 66-74 (2020). MSC: 60G15 60G20 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnitskiy} and \textit{O. O. Kurchenko}, Cybern. Syst. Anal. 56, No. 2, 223--230 (2020; Zbl 1456.60087); translation from Kibern. Sist. Anal. 2020, No. 2, 66--74 (2020) Full Text: DOI
Krasnitskiy, Sergey; Kurchenko, Oleksandr On Baxter type theorems for generalized random Gaussian fields. (English) Zbl 1423.60083 Silvestrov, Sergei (ed.) et al., Stochastic processes and applications. SPAS2017, Västerås and Stockholm, Sweden, October 4–6, 2017. Cham: Springer. Springer Proc. Math. Stat. 271, 91-103 (2018). MSC: 60G60 60F15 60F25 60G15 PDFBibTeX XMLCite \textit{S. Krasnitskiy} and \textit{O. Kurchenko}, Springer Proc. Math. Stat. 271, 91--103 (2018; Zbl 1423.60083) Full Text: DOI
Krasnitskiy, S. M.; Kurchenko, O. O. Baxter type theorems for generalized random Gaussian processes. (English) Zbl 1363.60057 Theory Stoch. Process. 21, No. 1, 45-52 (2016). MSC: 60G20 60G15 60G22 60H40 PDFBibTeX XMLCite \textit{S. M. Krasnitskiy} and \textit{O. O. Kurchenko}, Theory Stoch. Process. 21, No. 1, 45--52 (2016; Zbl 1363.60057)
Krasnits’kyj, Sergij M. On local conditions of equivalence of probabilistic measures corresponding to Gaussian homogeneous fields with power spectrum (the case of different mean values). (Ukrainian. English summary) Zbl 0990.60058 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2001, No. 4, 58-66 (2001). MSC: 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnits'kyj}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2001, No. 4, 58--66 (2001; Zbl 0990.60058)
Krasnitskyj, Sergij M. On conditions of equivalence of probabilistic measures corresponding to homogeneous Gaussian fields with different spectral densities of power type. (Ukrainian. English summary) Zbl 0990.60057 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2001, No. 3, 32-37 (2001). MSC: 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnitskyj}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2001, No. 3, 32--37 (2001; Zbl 0990.60057)
Krasnits’kyj, S. M. A sufficient condition for the equivalence of probability measures corresponding to Gaussian homogeneous random fields. (English. Ukrainian original) Zbl 0998.60036 Theory Probab. Math. Stat. 64, 85-91 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 75-81 (2001). Reviewer: N.M.Zinchenko (Kyïv) MSC: 60G30 PDFBibTeX XMLCite \textit{S. M. Krasnits'kyj}, Teor. Ĭmovirn. Mat. Stat. 64, 75--81 (2001; Zbl 0998.60036); translation from Teor. Jmovirn. Mat. Stat. 64, 75--81 (2001)
Krasnyts’kyj, Sergij M. On conditions of equivalence and singularity of probabilistic Gaussian measures corresponding to homogeneous fields with power spectrum. (Ukrainian. English summary) Zbl 0980.60064 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2001, No. 1, 33-42 (2001). MSC: 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnyts'kyj}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2001, No. 1, 33--42 (2001; Zbl 0980.60064)
Krasnyts’kyj, Sergij M. On conditions of equivalence of probabilistic Gaussian measures corresponding to homogeneous fields having power spectrum in the case of different correlation functions. (Ukrainian. English summary) Zbl 0980.60065 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2001, No. 2, 43-51 (2001). MSC: 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnyts'kyj}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2001, No. 2, 43--51 (2001; Zbl 0980.60065)
Krasnits’kyj, S. M. Gikhman-Skorokhod spectral conditions of equivalence of Gaussian measures corresponding to homogeneous random fields. (English. Ukrainian original) Zbl 1004.60034 Theory Probab. Math. Stat. 62, 65-76 (2001); translation from Teor. Jmovirn. Mat. Stat. 62, 61-71 (2000). Reviewer: A.V.Swishchuk (Kyïv) MSC: 60G30 60G57 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnits'kyj}, Teor. Ĭmovirn. Mat. Stat. 62, 61--71 (2000; Zbl 1004.60034); translation from Teor. Jmovirn. Mat. Stat. 62, 61--71 (2000)
Krasnitskij, S. M. Some comparative aspects of equivalence conditions of probability measures corresponding to ordinary and generalized random Gaussian fields. (English. Russian original) Zbl 1010.60045 Cybern. Syst. Anal. 36, No. 5, 691-698 (2000); translation from Kibern. Sist. Anal. 2000, No. 5, 68-78 (2000). Reviewer: B.L.S.Prakasa Rao (New Delhi) MSC: 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Cybern. Syst. Anal. 36, No. 5, 691--698 (2000; Zbl 1010.60045); translation from Kibern. Sist. Anal. 2000, No. 5, 68--78 (2000) Full Text: DOI
Krasnitskij, S. M.; Kryvyj, S. L. On sufficient equivalence conditions of Gaussian measures corresponding to homogeneous fields whose spectral densities have real zeros. (English. Russian original) Zbl 0974.60040 Cybern. Syst. Anal. 35, No. 6, 875-883 (1999); translation from Kibern. Sist. Anal. 1999, No. 6, 37-48 (1999). Reviewer: M.I.Yadrenko (Kyïv) MSC: 60G60 60G20 60G15 PDFBibTeX XMLCite \textit{S. M. Krasnitskij} and \textit{S. L. Kryvyj}, Cybern. Syst. Anal. 35, No. 6, 875--883 (1999; Zbl 0974.60040); translation from Kibern. Sist. Anal. 1999, No. 6, 37--48 (1999) Full Text: DOI
Krasnyts’kyj, S. M. On a spectral condition for the equivalence of Gaussian measures corresponding to random fields. (English. Ukrainian original) Zbl 0956.60010 Theory Probab. Math. Stat. 60, 95-104 (2000); translation from Teor. Jmovirn. Mat. Stat. 60, 85-94 (1999). Reviewer: Yu.V.Kozachenko (Kyïv) MSC: 60F15 60G42 PDFBibTeX XMLCite \textit{S. M. Krasnyts'kyj}, Teor. Ĭmovirn. Mat. Stat. 60, 85--94 (1999; Zbl 0956.60010); translation from Teor. Jmovirn. Mat. Stat. 60, 85--94 (1999)
Krasnitskij, S. M. On the conditions of equivalence of Gaussian measures corresponding to homogeneous random fields with different expectations. (Russian) Zbl 0936.60047 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1998, No. 2, 35-39 (1998). Reviewer: V.I.Masol (Kyïv) MSC: 60G60 62M40 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1998, No. 2, 35--39 (1998; Zbl 0936.60047)
Krasnitskyj, S. M. On some sufficient conditions for equivalence of Gaussian measures corresponding to generalized random fields. (English) Zbl 0948.60031 Methods Funct. Anal. Topol. 3, No. 2, 65-71 (1997). Reviewer: A.N.Kochubei (Kyïv) MSC: 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnitskyj}, Methods Funct. Anal. Topol. 3, No. 2, 65--71 (1997; Zbl 0948.60031)
Krasnitskij, S. M. Necessary and sufficient conditions of equivalence of probability measures corresponding to homogeneous random fields with spectral density. (English. Russian original) Zbl 0919.60010 Cybern. Syst. Anal. 33, No. 5, 641-646 (1997); translation from Kibern. Sist. Anal. 1997, No. 5, 36-44 (1997). Reviewer: Rimas Norvaiša (Vilnius) MSC: 60A10 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Cybern. Syst. Anal. 33, No. 5, 641--646 (1997; Zbl 0919.60010); translation from Kibern. Sist. Anal. 1997, No. 5, 36--44 (1997) Full Text: DOI
Krasnitskij, S. M. On necessary conditions of equivalence of Gaussian measures corresponding to homogeneous random fields. (English. Russian original) Zbl 0846.60050 Ukr. Math. J. 46, No. 6, 765-778 (1994); translation from Ukr. Mat. Zh. 46, No. 6, 708-719 (1994). MSC: 60G60 60G15 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Ukr. Mat. Zh. 46, No. 6, 708--718 (1994; Zbl 0846.60050); translation from Ukr. Mat. Zh. 46, No. 6, 708--719 (1994)
Krasnitskij, S. M. On a class of spectral conditions of equivalence of the Gaussian measures corresponding to homogeneous random fields. (Ukrainian. English summary) Zbl 0781.60040 Dopov. Akad. Nauk Ukr. 1993, No. 3, 37-39 (1993). MSC: 60G60 60G15 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Dopov. Akad. Nauk Ukr. 1993, No. 3, 37--39 (1993; Zbl 0781.60040)
Krasnitskij, S. M. Conditions for the equivalence of distributions of homogeneous Gaussian fields. (English. Russian original) Zbl 0703.60039 Theory Probab. Appl. 34, No. 4, 720-725 (1989); translation from Teor. Veroyatn. Primen. 34, No. 4, 786-791 (1989). MSC: 60G30 60G15 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Theory Probab. Appl. 34, No. 4, 720--725 (1989; Zbl 0703.60039); translation from Teor. Veroyatn. Primen. 34, No. 4, 786--791 (1989) Full Text: DOI
Krasnitskij, S. M. Conditions of the equivalence of distributions of homogeneous Gaussian fields. (Russian) Zbl 0694.60034 Teor. Veroyatn. Primen. 34, No. 4, 786-791 (1989). Reviewer: T.Inglot MSC: 60G30 60G15 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Teor. Veroyatn. Primen. 34, No. 4, 786--791 (1989; Zbl 0694.60034)
Krasnitskij, S. M.; Khilyuk, L. F. Stochastic problems of control of multipurpose reservoirs. (English. Russian original) Zbl 0592.93068 Sov. J. Autom. Inf. Sci. 18, No. 4, 60-67 (1985); translation from Avtomatika 1985, No. 4, 61-68 (1985). MSC: 93E20 86A05 90B15 PDFBibTeX XMLCite \textit{S. M. Krasnitskij} and \textit{L. F. Khilyuk}, Sov. J. Autom. Inf. Sci. 18, No. 4, 60--67 (1985; Zbl 0592.93068); translation from Avtomatika 1985, No. 4, 61--68 (1985)
Khilyuk, L. F.; Krasnitskij, S. M.; Matsak, I. K.; Ponomarenko, V. S.; Golovanov, I. N.; Popkov, N. V. Rational multicriterion planning for complex utilization of river-basin water resources (using the Dnieper river as an example). (English. Russian original) Zbl 0531.90057 Sov. Autom. Control 15, No. 3, 46-53 (1982); translation from Avtomatika 1982, No. 3, 47-55 (1982). MSC: 90B99 90C90 90B50 PDFBibTeX XMLCite \textit{L. F. Khilyuk} et al., Sov. Autom. Control 15, No. 3, 46--53 (1982; Zbl 0531.90057); translation from Avtomatika 1982, No. 3, 47--55 (1982)
Krasnitskij, S. M.; Khilyuk, L. F. Stochastic problem of optimal control for a cascade of water reservoirs. (English. Russian original) Zbl 0506.93078 Autom. Remote Control 43, 1078-1084 (1983); translation from Avtom. Telemekh. 1982, No. 8, 126-134 (1982). MSC: 93E20 90B15 93A99 90C35 93C10 PDFBibTeX XMLCite \textit{S. M. Krasnitskij} and \textit{L. F. Khilyuk}, Autom. Remote Control 43, 1078--1084 (1982; Zbl 0506.93078); translation from Avtom. Telemekh. 1982, No. 8, 126--134 (1982)
Krasnitskij, S. M. Some theorems on the solvability of an integral equation in the statistics of random fields. (English) Zbl 0486.60057 Theory Probab. Math. Stat. 21, 87-97 (1980). MSC: 60H20 60G60 45A05 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Theory Probab. Math. Stat. 21, 87--97 (1980; Zbl 0486.60057)
Krasnitskij, S. M. Correction to: Some examples of equivalent and orthogonal Gaussian distributions. (English) Zbl 0455.60034 Theory Probab. Appl. 25, 214 (1980). MSC: 60G15 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Theory Probab. Appl. 25, 214 (1980; Zbl 0455.60034) Full Text: DOI
Krasnitskij, S. M.; Khilyuk, L. F. On a stochastic problem of optimal control of water reservoirs. (English) Zbl 0437.93050 Sov. Autom. Control 12, No. 4, 34-40 (1979). MSC: 93E20 49K45 91B62 PDFBibTeX XMLCite \textit{S. M. Krasnitskij} and \textit{L. F. Khilyuk}, Sov. Autom. Control 12, No. 4, 34--40 (1979; Zbl 0437.93050)
Krasnitskij, S. M. Some examples of equivalent and orthogonal Gaussian distributions. (English) Zbl 0432.60044 Theory Probab. Appl. 24, 161-165 (1979). MSC: 60G15 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Theory Probab. Appl. 24, 161--165 (1979; Zbl 0432.60044) Full Text: DOI
Krasnitskij, S. M.; Khilyuk, L. F. On a stochastic optimal control problem for reservoirs. (Russian) Zbl 0421.93082 Avtomatika 1979, No. 4, 44-51 (1979). MSC: 93E20 PDFBibTeX XMLCite \textit{S. M. Krasnitskij} and \textit{L. F. Khilyuk}, Avtomatika 1979, No. 4, 44--51 (1979; Zbl 0421.93082)
Krasnitskij, S. M. Some theorems on the solution of an integral equation of random fields statistics. (Russian) Zbl 0412.60070 Teor. Veroyatn. Mat. Stat. 21, 75-86 (1979). MSC: 60H20 60G60 PDFBibTeX XML
Krasnitskii, S. M. Some examples of equivalent and orthogonal Gaussian distributions. (Russian) Zbl 0396.60039 Teor. Veroyatn. Primen. 24, 160-164 (1979). MSC: 60G15 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnitskii}, Teor. Veroyatn. Primen. 24, 160--164 (1979; Zbl 0396.60039)
Krasnitskiĭ, S. M. On the existence of a solution for an integral equation of the statistics of random fields. (Russian) Zbl 0429.60051 Teor. Sluch. Protsess. 6, 55-61 (1978). MSC: 60G60 45A05 45B05 PDFBibTeX XMLCite \textit{S. M. Krasnitskiĭ}, Teor. Sluch. Protsess. 6, 55--61 (1978; Zbl 0429.60051)
Krasnitskii, S. M. On an integral equation in the statistics of random fields. (English) Zbl 0394.60058 Theory Probab. Math. Stat. 9(1976), 115-126 (1977). MSC: 60G60 60G20 45A05 60G15 PDFBibTeX XMLCite \textit{S. M. Krasnitskii}, Theory Probab. Math. Stat. 9, 115--126 (1977; Zbl 0394.60058)
Krasnitskiĭ, S. M. On some limit theorems for random fields with Gaussian increments of the \(m\)th order. (English) Zbl 0348.60055 Theor. Probab. Math. Stat. 5 (1971, 1975), 73-82 (1976). MSC: 60G20 60G15 PDFBibTeX XML
Krasnitskij, S. M. On conditions for equivalence of probability measures corresponding to Gaussian fields differing in mean values. (English. Russian original) Zbl 0381.60008 Sov. Math., Dokl. 14, 1109-1111 (1973); translation from Dokl. Akad. Nauk SSSR 211, 779-780 (1973). MSC: 60B15 60G60 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Sov. Math., Dokl. 14, 1109--1111 (1973; Zbl 0381.60008); translation from Dokl. Akad. Nauk SSSR 211, 779--780 (1973)
Krasnitskij, S. M. On the conditions for equivalence of probability measures corresponding to Gaussian fields with different correlation functions. (English. Russian original) Zbl 0379.60011 Sov. Math., Dokl. 14, 1055-1057 (1973); translation from Dokl. Akad. Nauk SSSR 211, 528-529 (1973). MSC: 60B15 60G15 60G20 PDFBibTeX XMLCite \textit{S. M. Krasnitskij}, Sov. Math., Dokl. 14, 1055--1057 (1973; Zbl 0379.60011); translation from Dokl. Akad. Nauk SSSR 211, 528--529 (1973)
Krasnitskii, S. M. On conditions of equivalence and perpendicularity of measures corresponding to homogeneous Gaussian fields. (English. Russian original) Zbl 0334.60021 Theory Probab. Appl. 18, 588-592 (1973); translation from Teor. Veroyatn. Primen. 18, 615-621 (1973). MSC: 60G20 60G30 PDFBibTeX XMLCite \textit{S. M. Krasnitskii}, Theory Probab. Appl. 18, 588--592 (1973; Zbl 0334.60021); translation from Teor. Veroyatn. Primen. 18, 615--621 (1973) Full Text: DOI
Krasnitskiĭ, S. M. Über eine Integralgleichung der Statistik zufälliger Felder. (Russian) Zbl 0306.60025 Teor. Veroyatn. Mat. Stat. 9, 109-118 (1973). MSC: 60G25 45D05 PDFBibTeX XML
Krasnitskii, S. M. Über einige Grenzwertsätze für Zufallsfelder mit Gauß’schen Differenzen m-ter Ordnung. (Russian) Zbl 0299.60034 Teor. Veroyatn. Mat. Stat. 5, 71-80 (1971). MSC: 60G20 60G15 PDFBibTeX XML