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Teoriya Veroyatnostei i ee Primeneniya, 1974, Volume 19, Issue 3, Pages 514–532
(Mi tvp2924)
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This article is cited in 8 scientific papers (total in 8 papers)
Some results concerning small stochastic perturbations of dynamical systems.
Yu. I. Kifer Moscow
Abstract:
Let
$$
dx_t^\varepsilon=\varepsilon dw_t+b(x_t^\varepsilon)\,dt
$$
and $p^\varepsilon(t,x,y)$ be the transition probability density of $x_t^\varepsilon$. In section 1, we find an exact asymptotics of $p^\varepsilon(t,x,y)$ as $\varepsilon\to0$. Section 2 is devoted to investigation of the behaviour of $\mathbf P_x^\varepsilon\{x_\tau^\varepsilon\in\Delta,\ \tau\le T\}$ as $\varepsilon\to0$, where $\Delta$ is an open subset of the boundary $\Gamma$ of a bounded domain $G$ and $\tau$ is first exit time from $G$ $(x\in G)$.
Let $b(x)=Bx$, where $B$ is a matrix the eigenvalues of which have negative real parts. In this case we get an exact asymptotics of $\mathbf P_x^\varepsilon\{x_\tau^\varepsilon\in\Delta\}$ as $\varepsilon\to0$.
Received: 04.06.1973
Citation:
Yu. I. Kifer, “Some results concerning small stochastic perturbations of dynamical systems.”, Teor. Veroyatnost. i Primenen., 19:3 (1974), 514–532; Theory Probab. Appl., 19:3 (1975), 487–505
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Abstract page: | 175 | Full-text PDF : | 71 |
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