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In this paper, we prove that for a stochastic differential equation with the coefficients of class C ∞ , the successive approximations of Picard converge in the C ∞ -sense, which implies that the solution to stochastic differential equation is of class C ∞ in the initial value x almost surely. [ABSTRACT FROM AUTHOR]

Comparison theorems for solutions of one-dimensional backward stochastic differential equations were established by Peng and Cao-Yan, where the coefficients were, respectively, required to be Lipschitz and Dini continuous. In this work, we generalize the comparison theorem to the case where the coefficient is only continuous. [Copyright &y& Elsevier]