Professor G.L. Kulinich (09.12.1938 – 10.02.2022) – prominent scientist and teacher

O. D. Borysenko; S. V. Kushnirenko; Yu. S. Mishura; M. P. Moklyachuk; M. O. Perestyuk; V. G. Samoilenko; O. M. Stanzhytskyi; I. O. Shevchuk

doi:10.17721/1812-5409.2022/3.1

Authors

O. D. Borysenko Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-6670-8605
S. V. Kushnirenko Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-8390-5870
Yu. S. Mishura Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-6877-1800
M. P. Moklyachuk Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-6173-0280
M. O. Perestyuk Taras Shevchenko National University of Kyiv
V. G. Samoilenko Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-3267-2923
O. M. Stanzhytskyi Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-1456-729X
I. O. Shevchuk Taras Shevchenko National University of Kyiv https://orcid.org/0000-0003-1140-373X

DOI:

https://doi.org/10.17721/1812-5409.2022/3.1

Keywords:

Kulinich

Abstract

Pages of the article in the issue: 11 - 21

Language of the article: Ukrainian

References

Kulinich G., Kushnirenko S., Mishura Yu. Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations. Bocconi and Springer Series, Mathematics, Statistics, Finance and Economics, Vol. 9, 2020. – 248 p.

Kulinich, G. L.: Limit distributions of a solution of a stochastic diffusion equation. Theory Probab. Appl., 13, 478–482 (1968)

Kulinich, G. L.: Limit behavior of the distribution of the solution of a stochastic diffusion equation. Ukr. Math. J. 19, 231–235 (1968)

Kulinich, G. L.: Asymptotic normality of the distribution of the solution of a stochastic diffusion equation. Ukr. Math. J. 20, No. 3, 396–400 (1968)

Kulinich, G. L.: Limit theorem for the solution distribution of a stochastic differential equation. Dopov. Akad. Nauk Ukr. RSR, Ser. A, 1969, 118–121 (1969)

Kulinich, G. L.: The asymptotic behavior of the solution of a first order differential equation with a random right-hand side. Theory Probab. Math. Stat., 1, 128–140 (1970)

Kulinich, G. L.: On the asymptotic behavior of the distribution of the solution of a nonhomogeneous stochastic diffusion equation. Theory Probab. Math. Stat., 4, 95–102 (1971)

Kulinich, G. L.: Asymptotic behavior of the unstable solution of a stochastic homogeneous diffusion equation. Theory Probab. Math. Stat., 5, 81–87 (1971)

Kulinic, G. L.: A limit theorem on the distribution of the solution of a stochastic differential equation. Selected Transl. Math. Stat. Probab., 10, 54–58 (1972)

Kulinich, G. L.: The limit behavior of the solution of a system of stochastic differential equations without aftereffect. Theory Probab. Math. Stat., 7, 85–96 (1972)

Kulinich, G. L.: Certain limit theorem for stochastic differential equations that depend on a parameter. Theory Probab. Math. Stat., 9, 119–130 (1973)

Kulinich, G. L.: Limit distributions for functionals of integral type of unstable diffusion processes. Theory Probab. Math. Stat., 11, 81–85 (1974)

Kulinich, G. L.: On existence and uniqueness of a solution of a stochastic differential equation with martingale differential. Theory Probab. Appl., 19, 168–171 (1974)

Kulinich, G. L.: Certain limit theorems for a sequence of Markov chains. Theory Probab. Math. Stat., 12, 77–89 (1975)

Kulinich, G. L.: On the estimation of the drift parameter of a stochastic diffusion equation. Theory Probab. Appl., 20, 384–387 (1975)

Kulinich, G. L.: On the asymptotic behavior of the distribution of the solution of a nonhomogeneous stochastic diffusion equation. Theory Probab. Math. Stat., 14, 87–94 (1976)

Kulini˘c, G. L.: The asymptotic behavior of the unstable solution of the one-dimensional stochastic diffusion equation. Theory Probab. Math. Stat., 15, 83–89 (1976)

Koval’chuk, O. P., Kulinich, G. L.: On the asymptotic behaviour of distributions for functionals on the argument of the solution of two-dimensional system of linear stochastic diffusion equations. Dopov. Akad. Nauk Ukr. RSR, Ser. A, 1977, 689–693 (1977)

Kulinich, G. L.: On the limit behaviour of solutions of stochastic differential equations of diffusion type with random coefficients. Limit Theor. for Random Process., Akad. Nauk Ukr. SSR, Inst. Mat., 137–151 (1977)

processes. Theory Probab. Math. Stat., 14, 79–83 (1977)

Kulinich, G. L.: Limit theorems for one-dimensional stochastic differential equations with nonregular dependence of the coefficients on a parameter. Theory Probab. Math. Stat., 15, 101–115 (1978)

Kulinich, G. L.: On the asymptotic behavior of the solution of the one-dimensional stochastic diffusion equation. Stochastic differential systems, Proc. IFIP-WG 7/1 Work. Conf., Vilnius/Lith. 1978, Lect. Notes Control Inf. Sci. 25, 334–343 (1980)

Kulinich, G. L., Le Thieng Huong: On the construction and limit behavior of a multiple stochastic integral of a diffusion process. Theory Probab. Appl., 25, 597–604 (1981)

Kulinich, G. L.: Convergence of the solution of a one-dimensional stochastic diffusion equation to Bessel’s diffusion process. Analytical methods of investigation in probability theory, Collect. Sci. Works, Kiev, 106-113 (1981)

Kulinich, G. L.: On necessary and sufficient conditions for convergence of solutions to one- dimensional stochastic diffusion equations with a non-regular dependence of the coefficients on a parameter. Theory Probab. Appl., 27, No. 4, 856–862 (1983)

Kulinich, G. L.: Limit behaviour of solutions of stochastic diffusion equations when the convergence of the coefficients is non-regular. Probability theory and mathematical statistics, Proc. 4th USSR - Jap. Symp., Tbilisi/USSR 1982, Lect. Notes Math. 1021, 352–354 (1983)

Kulinich, G. L.: Limit behavior of a random harmonic oscillator. Visn. Ky¨ıv. Univ., Mat. Mekh., 25, 128–138 (1983)

Kulinich, G. L., Petrov, I. B.: On the limit behavior of the absolute value of some of the components of a system of Itˆo stochastic diffusion equations. Theory Probab. Math. Stat., 28, 79–87 (1984)

Kulinich, G. L.: On the law of the iterated logarithm for one-dimensional diffusion processes. Theory Probab. Appl., 29, 563–566 (1985)

Divnich, N. T., Kulinich, G. L.: On limit behaviour of the solution of the Cauchy problem for parabolic equations with random right side. Theory Stoch. Process., 13, 25–28 (1985)

Almazov, M., Kulinich, G. L.: Asymptotic behaviour of an unstable solution of the non-homogeneous stochastic diffusion equation. Theory Stoch. Process., 15, 3–10 (1987)

Almazov, M., Kulinich, G. L.: Limit theorems for one-dimensional nonhomogeneous stochastic diffusion equations under irregular dependence of the coefficients on a parameter. Ukr. Math. J., 42, No. 4, 383–390 (1990)

Kulinich, G. L., Kharkova, M. V.: On asymptotic behaviour of solutions of systems of stochastic diffusion equations in case of irregular dependence of coefficients on a parameter. Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 6, 19–22 (1990)

Almazov, M., Kulinich, G. L.: On the asymptotic behavior of an unstable solution of an inhomogeneous stochastic diffusion equation. J. Sov. Math., 53, No. 4, 345–352 (1991)

Kulinich, G. L., Mynbaeva, M. U.: On space averaging of parabolic equations. Ukr. Math. J., 44, No. 4, 561–564 (1992)

Kulinich, G. L., Denisova, J. Yu.: Behaviour of a solution of a system of stochastic differential equations. Random Oper. Stoch. Equ.,1, No. 1, 23–28 (1993)

Kulinich, G. L., Kharkova, M. V.: Limit theorems for stochastic differential equations without after-effect. Theory Probab. Appl., 40, No.3, 523–541 (1993)

Kulinich, G. L., Munbayeva, M. U.: Limit behavior of Cauchy problem solution of parabolic equation. Random Oper. Stoch. Equ., 2, No.3, 225–234 (1994)

Kulinich, G.: On necessary and sufficient conditions for convergence of homogeneous additi- ve functionals of diffusion processes. New trends in probability and mathematical statistics. Proceedings of the second Ukrainian-Hungarian conference, Mukachevo, Ukraine, September 25– October 1, 1992. Kiev: TViMS, 381–390 (1995)

Kulinich, G. L.: On the limiting behavior of a harmonic oscillator with random external disturbance. J. Appl. Math. Stochastic Anal., 8, No. 3, 265–274 (1995)

Kulinich, G. L.: Qualitative analysis of the influence of random perturbations on the phase velocity of the harmonic oscillator. Random Oper. Stoch. Equ., 3, No. 2, 141–152 (1995)

Kulinich, G. L., Kas’kun, E. P.: On the asymptotic behavior of solutions of a certain class of one-dimensional Itˆo stochastic differential equations. Theory Probab. Math. Stat., 56, 96–104 (1997)

Kulinich, G. L.: On invariant sets of the second-order systems of stochastic Itˆo’s equations. Dopov. Akad. Nauk Ukr., No. 10, 35–39 (1997)

Kulinich, G. L.: Qualitative analysis of the influence of random perturbations of “white noise” type applied along the vector of phase velocity on a harmonic oscillator with friction. Ukr. Math. J., 49, No. 1, 36–47 (1997)

Kulinich, G. L., Kaskun, E. P.: On the asymptotic behavior of solutions of one-dimensional Ito’s stochastic differential equations with singularity points. Theory Stoch. Process., 4(20), No. 1-2, 189–197 (1998)

Kulinich, G. L.: Qualitative analysis of the behavior of a harmonic oscillator under the action of white or shot noises. Theory Probab. Math. Stat., 58, 81–91 (1998)

Kulinich, G. L., Kushnirenko, S. V.: On the stabilization of the energy of a harmonic oscillator disturbed by random processes of the “white and shot noises” types. J. Appl. Math. Stochastic Anal., 13, No. 1, 25–31 (2000)

Kulinich, G. L., Pereguda, O. V.: Qualitative analysis of systems of Itˆo stochastic differential equations. Ukr. Math. J., 52, No. 9, 1251–1256 (2000)

Kulinich, G. L., Almazov, M.: On convergence of solutions of stochastic diffusion equations with unlimited increasing drift coefficients on finite segments. Ky¨ıv: Institute of Mathematics of NAS of Ukraine, Skorokhod’s ideas in probability theory, 241–247 (2000)

Kulinich, G. L., Bernatskaya, Yu. V.: On the phase portrait of a harmonic oscillator with friction perturbed by a random process of white noise type. Math. Notes, 68, No.6, 730–736 (2000)

Kulinich, G. L., Kushnirenko, S. V.: Invariant sets for systems of stochastic differential equations without aftereffect. Theory Probab. Math. Stat., 63, 112–118 (2000)

Kulinich, G. L., Bernats’ka, Yu. V.: On stabilization of energy of a conservative system perturbed by a random “white noise” type process in the Itˆo form. Ukr. Math. J., 53, No. 10, 1429–1435 (2001)

Kulinich, G. L., Kushnirenko, S. V.: On the stabilization of a solution of the Cauchy problem for a class of integro-differential equations. Ukr. Math. J., 56, No. 12, 1699–1706 (2004)

Kulinich, G. L., Kushnirenko, S. V.: Invariant sets of systems of stochastic differential equations with jumps. Nonlinear Oscillations, 8, No. 2, 234–240 (2005)

Kulinich, H. L., Ershov, A. V.: On stability of sets for sequences of random polygonal lines. Nonlinear Oscillations, 9, No. 3, 346–357 (2006)

Kulinich, G. L., Kushnirenko, S. V.: The first integrals for systems of stochastic differential equations with jumps. Theory Probab. Math. Stat., 76, 84–91 (2007)

Kulinich, G. L., Yershov, A. V.: Convergence of a sequence of Markov chains to a diffusion type process. Theory Probab. Math. Stat., 78, 103–118 (2008)

Kulinich, H. L., Kurovs’kyi, D. Yu., Petrusenko, D. V.: Asymptotic analysis of the mathemati- cal expectation of the total energy of a harmonic oscillator under random pulse perturbation. Nonlinear Oscillations, 12, No. 3, 305–313 (2009)

Korolyuk, V. S., Zakuzylo, O. K., Gorodnij, M. F., Kartashov, M. V., Kozachenko, Yu. V. , Kulinich, G. L., Mishura, Yu. S., Moklyachuk, M. P., Radchenko, V. M., Vyshens’kyj, V. A.: Anatolij Volodymyrovych Skorokhod (10.09.1930–03.01.2011). Visn., Mat. Mekh., Ky¨ıv. Univ. Im. Tarasa Shevchenka, No. 26, 62–63 (2011)

Kulinich, G. L., Kushnirenko, S. V.: Strong uniqueness of solutions of stochastic differential equations with jumps and non-Lipschitz random coefficients. Modern Stochastics: Theory and Appl. 1, No. 1, 65–72 (2014)

Kulinich, G. L., Kushnirenko, S. V., Mishura, Y. S.: Asymptotic behavior of the integral functi- onals for unstable solutions of one-dimensional Ito stochastic differential equations. Theory Probab. Math. Stat. 89, 101–114 (2014)

Kulinich, G. L., Kushnirenko, S. V., Mishura, Y. S.: Asymptotic behavior of the martingale type integral functionals for unstable solutions to stochastic differential equations. Theory Probab. Math. Stat. 90, 115–126 (2015)

Kulinich, G. L., Kushnirenko, S. V., Mishura, Y. S.: Limit behavior of functionals of diffusion type processes. Theor. Probab. Math. Stat., 92, 93–107 (2016)

Kulinich, G. L., Kushnirenko, S. V., Mishura, Y. S.: Asymptotic behavior of homogeneous additive functionals of the solutions of Ito stochastic differential equations with nonregular dependence on parameter. Modern Stoch., Theory Appl., 3, No. 2, 191–208 (2016)

Kulinich, G., Kushnirenko, S.: Asymptotic behavior of functionals of the solutions to inhomogeneous Itˆo stochastic differential equations with nonregular dependence on parameter. Modern Stoch., Theory Appl., 4, No. 3, 199–217 (2017)

Kulinich, G. L., Kushnirenko, S. V., Mishura, Yu. S.: Weak convergence of integral functionals constructed from solutions of Itˆo’s stochastic differential equations with non-regular dependence on a parameter. Theory Probab. Math. Stat., 96, 111–125 (2018)

Kulinich, G. L., Zimin, O. I.: About asymptotic behaviour of the mathematical expectation of the total energy of the harmonic oscillator with random perturbation. Visn., Ser. Fiz.-Mat. Nauky, Ky¨ıv. Univ. Im. Tarasa Shevchenka, No. 3, 47–52 (2018)