Abstract
For stochastic differential equations with non-Lipschitz diffusion (degenerated) coeffcients and non-Lipschitz drift coefficients, which absolute value can be very much greater than linear growth, the existence of weak, strong solution is obtained under some rather weak conditions, respectively. Then the existence of an optimal (pathwise) Bang-Bang control for a very much non-linear degenerated stochastic system is derived. The technique used here is the martingale approach, local time method, and comparison theorem.
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