On the asymptotic behaviour of solutions of stochastic differential equations - Keller, Gerhard; Kersting, Götz; Rösler, Uwe (Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 1984)
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.