Large deviation principle for backward stochastic differential equations with a stochastic Lipschitz condition on z

被引：1

作者：

Shi, Yufeng ^{[1
,2
]}

Wen, Jiaqiang ^{[3
,4
]}

Yang, Zhi ^{[5
]}

机构：

[1] Shandong Univ, Inst Financial Studies, Natl Ctr Appl Math Shandong, Jinan 250100, Shandong, Peoples R China

[2] Shandong Univ, Natl Ctr Appl Math Shandong, Sch Math, Jinan 250100, Shandong, Peoples R China

[3] Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China

[4] Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen 518055, Guangdong, Peoples R China

[5] Shandong Univ, Inst Financial Studies, Jinan 250100, Shandong, Peoples R China

来源：

STOCHASTICS AND DYNAMICS | 2024年 / 24卷 / 06期

基金：

中国国家自然科学基金; 国家重点研发计划;

关键词：

Quadratic BSDEs; parabolic PDEs; Feynman-Kac formula; Malliavin calculus; large deviation principle; QUADRATIC BSDES;

D O I：

10.1142/S0219493724500436

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we provide a probabilistic interpretation of the viscosity solution of a parabolic partial differential equation through the solution of a class of quadratic backward stochastic differential equations (BSDEs). Additionally, we demonstrate the convergence and the large deviation principle for the solutions of these quadratic BSDEs, which are linked to a family of Markov processes with diffusion coefficients that tend toward zero.

引用

页数：29

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