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Adapted solutions of backward stochastic differential equations with non- Lipschitz coefficients. (English) Zbl 0835.60049
The author considers the following backward stochastic differential equation $$x(t) = \int^1_tf \bigl( s,x(s), y(s) \bigr) ds + \int^1_t \biggl[ g \bigl( s,x (s) \bigr) + y( s) \biggr] dw(s) = X \tag *$$ on $0 \le t \le 1$. Here $w(t)$ in a $q$-dimensional Brownian motion and $y(t)$ is an adapted control process. He gives a theorem on the existence and uniqueness of the solution for (*) under a weaker condition than the Lipschitz one.
Reviewer: J.H.Kim (Pusan)

60H10Stochastic ordinary differential equations
Full Text: DOI
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