Multidimensional BSDEs with uniformly continuous coefficients: the general result

2015/08/26 by Li, Min, Shi, Yufeng
#60H10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1508.06671

Abstract

In this paper, by introducing a new notion of envelope of the stochastic process, we construct a family of random differential equations whose solutions can be viewed as solutions of a family of ordinary differential equations and prove that the multidimensional backward stochastic differential equations (BSDEs for short) with the general uniformly continuous coefficients are uniquely solvable. As a result, we solve the open problem of multidimensional BSDEs with uniformly continuous coefficients.

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