On the φ-asymptotic behaviour of solutions of stochastic differential equations

• Date: 2008
• Main Authors: Buldygin, V.V., Klesov, O.I., Steinebach, J.G., Tymoshenko, O.A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/4532
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the φ-asymptotic behaviour of solutions of stochastic differential equations / V.V. Buldygin, O.I. Klesov, J.G. Steinebach, O.A. Tymoshenko // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 1. — С. 11–29. — Бібліогр.: 28 назв.— англ.

In this paper we study the a.s. asymptotic behaviour of the solution of the stochastic dfferential equation dX(t) = g(X(t))dt +σ(X(t))dW(t), X(0) = b > 0, where g and σ are positive continuous functions and W is a Wiener process. Making use of the theory of pseudo-regularly varying (PRV) function...