A representation theorem for generators of BSDEs with general growth generators in y and its applications

作者：Xiao, Lishun; Fan, Shengjun^*

来源：Statistics & Probability Letters, 2017, 129: 297-305.

DOI：10.1016/j.spl.2017.06.014

• Backward stochastic differential equation
• Representation theorem
• General growth
• Weak monotonicity
• Viscosity solution

In this paper we first prove a general representation theorem for generators of backward stochastic differential equations (BSDEs for short) by utilizing a localization method involved with stopping time tools and approximation techniques, where the generators only need to satisfy a weak monotonicity condition and a general growth condition in y and a Lipschitz condition in z. This result basically solves the problem of representation theorems for generators of BSDEs with general growth generators in y. Then, such representation theorem is adopted to prove a probabilistic formula, in viscosity sense, of semilinear parabolic PDEs of second order. The representation theorem approach seems to be a potential tool to the research of viscosity solutions of PDEs.

• 出版日期2017-10
• 单位中国矿业大学（北京）; 徐州医科大学