Yuskovych V. Asymptotic behavior of solutions of stochastic differential equations in multidimensional space

Українська версія

Thesis for the degree of Doctor of Philosophy (PhD)

State registration number

0824U002530

Thesis Registration Form

0824U002530.pdf

Applicant for

Specialization

  • 111 - Математика

Specialized Academic Board

ДФ 26.002.180; ID 6414

National Technscal University of Ukraine "Kiev Polytechnic Institute".

Essay

The main results of this dissertation relate to the asymptotic behavior almost surely (abbreviated as “a.s.”), as time goes to infinity, of solutions of multidimensional stochastic differential equations (after this referred to as SDE) with Wiener noise. We study the asymptotic behavior of the solution of the multidimensional SDE with the help of two components: the behavior of the norm and the behavior of the angle. Consider the case when the drift coefficient has some power-law asymptotics and the diffusion coefficient is bounded by some power-law function. In the dissertation, we present sufficient conditions, in terms of the coefficients of the SDE, such that a.s. the solution norm goes to infinity, the solution angle stabilizes, and the asymptotics of the solution norm is some power function (perhaps depending on the limit angle) having the form similar to the asymptotics of the solution of the corresponding ordinary differential equation.

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Research papers

Yuskovych V. “On the Asymptotics of Solutions of Stochastic Differential Equations with Jumps”. Ukrainian Mathematical Journal 75 (2024): 1778-1795.

Yuskovych V. K. “On asymptotic behavior of solutions of stochastic differential equations in multidimensional space”. Theory of Stochastic Processes 27.1 (2023): 53-66.

Юськович В. К. «Асимптотична поведінка розв'язків стохастичних диференціальних рівнянь у багатовимірному просторі». X всеукраїнська наукова конференція молодих математиків (16-17 квітня 2021, дистанційно): 55.

Yuskovych V. “On Asymptotic Behavior of Solutions of Stochastic Differential Equations in Multidimensional Space”. Modern Stochastics: Theory and Applications V (June 1-4, 2021, online): 115.

Yuskovych V. “Asymptotic behaviour of solutions of multidimensional stochastic differential equations”. International Conference of Young Mathematicians (June 1-3, 2023, online).

Юськович В. К. «Про асимптотику розв'язків стохастичних диференціальних рівнянь зі стрибками». XIX міжнародна наукова конференція ім. академіка М. Кравчука (11-12 жовтня 2023, дистанційно): 187.

Yuskovych V. K. “On asymptotics of solutions of stochastic differential equations with jumps”. International Uzbek-Ukrainian conference “Modern problems of the theory of stochastic processes and their applications” (October 10-11, 2023, online): 49.

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