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The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) in R p (p ∈ [1, ∞)) and backward stochastic differential equations (BSDEs) in R p × H p (p ∈ (1, ∞)) and in R ∞ × H ∞ BM O , with the coefficients being allowed to be unbounded. In particular, the probabilistic version of Fefferman's inequality(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)