郑石秋, 李寿梅. 生成元连续且线性增长的反射倒向随机微分方程生成元的表示定理[J]. 应用概率统计, 2017, 33(6): 551-566. DOI: 10.3969/j.issn.1001-4268.2017.06.001
引用本文: 郑石秋, 李寿梅. 生成元连续且线性增长的反射倒向随机微分方程生成元的表示定理[J]. 应用概率统计, 2017, 33(6): 551-566. DOI: 10.3969/j.issn.1001-4268.2017.06.001
ZHENG ShiQiu, LI ShouMei. Representation Theorems for RBSDEs with Continuous Generators[J]. Chinese Journal of Applied Probability and Statistics, 2017, 33(6): 551-566. DOI: 10.3969/j.issn.1001-4268.2017.06.001
Citation: ZHENG ShiQiu, LI ShouMei. Representation Theorems for RBSDEs with Continuous Generators[J]. Chinese Journal of Applied Probability and Statistics, 2017, 33(6): 551-566. DOI: 10.3969/j.issn.1001-4268.2017.06.001

生成元连续且线性增长的反射倒向随机微分方程生成元的表示定理

Representation Theorems for RBSDEs with Continuous Generators

  • 摘要: 本文建立了一个生成元满足连续且线性增长条件的反射倒向随机微分方程生成元的局部表示定理,此定理推广了一些已有的倒向随机微分方程生成元的表示定理. 应用此表示定理, 本文获得了一个一般的反射倒向随机微分方程的逆比较定理,同时讨论了此类方程的一些性质.

     

    Abstract: In this paper, we establish a local representation theorem for generators of reflected backward stochastic differential equations (RBSDEs), whose generators are continuous with linear growth. It generalizes some known representation theorems for generators of backward stochastic differential equations (BSDEs). As some applications, a general converse comparison theorem for RBSDEs is obtained and some properties of RBSDEs are discussed.

     

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