On the asymptotic behaviour of solutions of stochastic differential equations

Keller G, Kersting G, Rösler U (1984)

Publication Type: Journal article, Original article

Publication year: 1984

Journal

Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete Springer Verlag

Publisher: Springer Verlag

Book Volume: 68

Pages Range: 163--189

Journal Issue: 2

DOI: 10.1007/BF00531776

Abstract

In this paper we study the asymptotic behaviour of the solution of the stochastic differential equation dX t=g(X t)dt+σ(X t)dW t, where σ and g are positive functions and W tis a Wiener process. We clarify, under which conditions X tmay be approximated on {X t→∞} by means of a deterministic function. Further the question is treated, whether X tconverges in distribution on {X t→∞. We deal with the Ito-solution as well as the Stratonovitch-solution and compare both.

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Goethe-Universität Frankfurt am Main DE Germany (DE) Christian-Albrechts-Universität zu Kiel DE Germany (DE)

How to cite

APA:

Keller, G., Kersting, G., & Rösler, U. (1984). On the asymptotic behaviour of solutions of stochastic differential equations. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 68(2), 163--189. https://doi.org/10.1007/BF00531776

MLA:

Keller, Gerhard, Götz Kersting, and Uwe Rösler. "On the asymptotic behaviour of solutions of stochastic differential equations." Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 68.2 (1984): 163--189.

BibTeX: Download