具有扩散约束的BSDEs和具有无界数据的粘性Hamilton-Jacobi方程

IF 1.2 2区数学 Q2 STATISTICS & PROBABILITY

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-05-26 DOI:10.1214/16-AIHP762

Andrea Cosso, H. Pham, Hao Xing

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引用次数: 8

摘要

通过一类在鞅部分有约束的倒向随机微分方程，给出了一类梯度项具有凸性和超线性非线性的粘性Hamilton-Jacobi (HJ)方程的随机表示。我们将结果与经典的(超)二次BSDE表示形式进行了比较，并特别证明了在更一般的系数增长假设下，粘性HJ方程的解的存在性，包括无界扩散系数和终端数据。

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BSDEs with diffusion constraint and viscous Hamilton–Jacobi equations with unbounded data

We provide a stochastic representation for a general class of viscous Hamilton-Jacobi (HJ) equations, which has convexity and superlinear nonlinearity in its gradient term, via a type of backward stochastic differential equation (BSDE) with constraint in the martingale part. We compare our result with the classical representation in terms of (super)quadratic BSDE, and show in particular that existence of a solution to the viscous HJ equation can be obtained under more general growth assumptions on the coefficients, including both unbounded diffusion coefficient and terminal data.

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来源期刊

Annales De L Institut Henri Poincare-probabilites Et Statistiques 数学-统计学与概率论

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.