Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Asymptotic stability and spiraling properties for solutions of stochastic equations


Authors: Avner Friedman and Mark A. Pinsky
Journal: Trans. Amer. Math. Soc. 186 (1973), 331-358
MSC: Primary 60H10; Secondary 60J60
MathSciNet review: 0329031
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a system of Itô equations in a domain in $ {R^d}$. 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 \to \infty $. In the case of plane domains, we give conditions to ensure that the process ``spirals"; the angle obeys the strong law of large numbers.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60H10, 60J60

Retrieve articles in all journals with MSC: 60H10, 60J60


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0329031-5
Keywords: Stochastic differential equation, diffusion process, asymptotic stability, spiraling solutions
Article copyright: © Copyright 1973 American Mathematical Society