2019
Том 71
№ 11

All Issues

Kolesnik A. D.

Articles: 1
Article (Russian)

Asymptotic relation for the density of a multidimensional random evolution with rare poisson switchings

Kolesnik A. D.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 12. - pp. 1631 – 1641

In the Euclidean space $\mathbb{R}^m,\quad m \geq 2,$ the symmetric random evolution $\textbf{X}(t) = (X_1(t),...,X_m(t))$ controlled by a homogeneous Poisson process with parameter $\lambda > 0$ is considered.
An asymptotic formula for the transition density $p(\textbf{x},t),\quad t > 0,$ of the process $\textbf{X}(t)$ for $\lambda \rightarrow 0$ is obtained. The behavior of $p(\textbf{x},t)$ near the boundary of the diffusion area in spaces of various dimensions is described.