Weak solutions of backward stochastic differential equations with continuous generator

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Bouchemella, Nadira¹  de Fitte, Paul Raynaud¹ 

[1] Normandie Univ, Lab Raphael Salem, UMR CNRS 6085, Rouen, France

关键词: Weak solution;    Joint solution measure;    Young measure;    Jakubowski's topology S;    Condition UT;    Meyer-Zheng;    Yamada-Watanabe-Engelbert;   

DOI  :  10.1016/j.spa.2013.09.011

来源: Elsevier

【 摘 要 】

We prove the existence of a weak solution to a backward stochastic differential equation (BSDE) Y-t = xi + integral(T)(t) f(s, X-s, Y-s, Z(s)) ds -integral(T)(t) Z(s)dW(s) in a finite-dimensional space, where f (t, x, y, z) is affine with respect to z, and satisfies a sublinear growth condition and a continuity condition. This solution takes the form of a triplet (Y, Z, L) of processes defined on an extended probability space and satisfying Y-t = xi + integral(T)(t) f(s, X-s, Y-s, Z(s)) ds -integral(T)(t) Z(s)dW(s) - (L-T - L-t) where L is a martingale with possible jumps which is orthogonal to W. The solution is constructed on an extended probability space, using Young measures on the space of trajectories. One component of this space is the Skorokhod space D endowed with the topology S of Jakubowski. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free