On existence and uniqueness of solutions to uncertain backward stochastic differential equations

2014/01/29 by Fei, Weiyin
#60H10 #94D05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1401.7403

Abstract

This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in modelling hybrid systems, where the phenomena are simultaneously subjected to two kinds of uncertainties: randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coefficients are proved.

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