Asymptotic stability and spiraling properties for solutions of stochastic equations

Avner Friedman; Mark A. Pinsky

doi:10.1090/S0002-9947-1973-0329031-5

Asymptotic stability and spiraling properties for solutions of stochastic equations

Avner Friedman, Mark A. Pinsky

Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We consider a system of Ito equations in a domain in The boundary consists of points and closed surfaces. The coefficients are such that, starting for the exterior of the domain, the process stays in the exterior. We give sufficient conditions to ensure that the process converges to the boundary when t—In the case of plane domains, we give conditions to ensure that the process "spirals”; the angle obeys the strong law of large numbers.

Original language	English (US)
Pages (from-to)	331-358
Number of pages	28
Journal	Transactions of the American Mathematical Society
Volume	186
DOIs	https://doi.org/10.1090/S0002-9947-1973-0329031-5
State	Published - Dec 1973

Keywords

Asymptotic stability
Diffusion process
Spiraling solutions
Stochastic differential equation

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-1973-0329031-5

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AU - Pinsky, Mark A.

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AB - We consider a system of Ito equations in a domain in The boundary consists of points and closed surfaces. The coefficients are such that, starting for the exterior of the domain, the process stays in the exterior. We give sufficient conditions to ensure that the process converges to the boundary when t—In the case of plane domains, we give conditions to ensure that the process "spirals”; the angle obeys the strong law of large numbers.

KW - Asymptotic stability

KW - Diffusion process

KW - Spiraling solutions

KW - Stochastic differential equation

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JF - Transactions of the American Mathematical Society

ER -

Asymptotic stability and spiraling properties for solutions of stochastic equations

Abstract

Keywords

ASJC Scopus subject areas

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