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This paper studies, under some natural monotonicity conditions, the theory (existence and uniqueness, a priori estimate, continuous dependence on a parameter) of forward–backward stochastic differential equations and their connection with quasilinear parabolic partial differential equations. We use a purely probabilistic approach, and allow the forward(More)
This paper concerns partially observed optimal control of possibly degenerate stochas-tic differential equations, with correlated noises between the system and the observation. The control is allowed to enter into all the coefficients. A general maximum principle is proved for the partially observed optimal control, and the relations among the adjoint(More)
A Dynkin game is considered for stochastic differential equations with random coefficients. We first apply Qiu and Tang's maximum principle for backward stochastic partial differential equations to generalize Krylov estimate for the distribution of a Markov process to that of a non-Markov process, and establish a generalized Itô-Kunita-Wentzell's formula(More)
We obtain the global existence and uniqueness result for a one-dimensional backward stochastic Riccati equation, whose generator contains a quadratic term of L (the second unknown component). This solves the one-dimensional case of Bismut-Peng's problem which w as initially proposed by Bismut (1978) in the Springer yellow book LNM 649. We use an(More)