arXiv subjects
Publications and source records attributed to Vitalii A. Gasanenko.
We lead the algorithm of expansion of sojourn probability of many-dimensional diffusion processes in small domain. The principal member of this expansion defines normalizing coefficient for special limit theorems.
This paper is devoted to the study of the following problem. We have set of diffusion processes with absorption on boundaries in some region at initial time $t=0$. It is required to estimate of number of the unabsorbed processes for the fixed time ~$τ>0$. The number of initial processes is considered as function of $τ$ and $τ\to\infty$.
We prove constructible sufficient conditions of lack of exit by solutions of stochastic differential Ito's equations from domains with smooth boundaries
We have random number of independent diffusion processes with absorption on boundaries in some region at initial time $t=0$. The initial numbers and positions of processes in region is defined by Poisson random measure. It is required to estimate of number of the unabsorbed processes for the fixed time \~$τ>0$. The Poisson random measure depends on $τ$ and $τ\to\infty$.
This paper deals with study of the sufficient condition of approximation raring process with mixing by renewall process. We consider use the proved results to practice problem too