PRV property and the asymptotic behaviour of solutions of stochastic differential equations

• Date: 2005
• Main Authors: Buldygin, V.V., Klesov, O.I., Steinebach, J.G.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2005
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/4424
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: PRV property and the asymptotic behaviour of solutions of stochastic differential equations / V.V. Buldygin, O.I. Klesov, J.G. Steinebach // Theory of Stochastic Processes. — 2005. — Т. 11 (27), № 3-4. — С. 42–57. — Бібліогр.: 17 назв.— англ.

We consider the a.s. asymptotic behaviour of a solution of the stochastic differential
 equation (SDE) dX(t) = g(X(t))dt + σ(X(t))dW(t), with X(0) ≡ b > 0, where g(.)
 and σ(.) are positive continuous functions and W(.) is the standard Wiener process.
 By applying the theo...