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Well-posedness of scalar BSDEs with sub-quadratic generators and related PDEs
Stochastic Processes and their Applications ( IF 1.4 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.spa.2020.09.001
Shengjun Fan , Ying Hu

Abstract We first establish the existence of an unbounded solution to a backward stochastic differential equation (BSDE) with generator g allowing a general growth in the state variable y and a sub-quadratic growth in the state variable z , when the terminal condition satisfies a sub-exponential moment integrability condition, which is weaker than the usual exp ( μ L ) -integrability and stronger than L p ( p > 1 ) -integrability. Then, we prove the uniqueness and comparison theorem for the unbounded solutions of the preceding BSDEs under some additional assumptions and establish a general stability result for the unbounded solutions. Finally, we derive the nonlinear Feynman–Kac formula in this context.

中文翻译:

具有次二次生成器和相关 PDE 的标量 BSDE 的适定性

摘要 我们首先建立了反向随机微分方程 (BSDE) 的无界解的存在性,生成器 g 允许状态变量 y 的一般增长和状态变量 z 的次二次增长,当终端条件满足子-指数矩可积性条件,比通常的 exp ( μ L ) - 可积性弱,强于 L p ( p > 1 ) - 可积性。然后,我们在一些附加假设下证明了上述 BSDE 的无界解的唯一性和比较定理,并建立了无界解的一般稳定性结果。最后,我们在此背景下推导出非线性 Feynman-Kac 公式。
更新日期:2021-01-01
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