On existence and stability of weak solutions of multidimensional stochastic differential equations with measurable coefficients. (English) Zbl 0728.60066

Rozkosz, Andrzej; Słomiński, Leszek

Stochastic Processes Appl. 37, No. 2, 187-197 (1991).

In the present paper the authors have studied the stochastic equations of the type \[ (*)\quad X_ t=x+\int^{t}_{0}B(X_ s)dM_ s+\int^{t}_{0}A(X_ s)d<M>_ s,\quad t\in R^+, \] where \(M=(M^ 1,...,M^ d)\) is a d-dimensional continuous local martingale and the coefficients A, B are noncontinuous. The results on the existence and weak convergence of the solutions of (*) are given under some suitable conditions on the functions involved in (*).

Reviewer: B.G.Pachpatte (Aurangabad)

MSC:

60H20	Stochastic integral equations
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60F05	Central limit and other weak theorems
60J60	Diffusion processes

Keywords:

continuous local martingale; weak convergence of the solutions

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