ON QUASILINEAR PARABOLIC SYSTEMS AND FBSDES OF QUADRATIC GROWTH

被引：0

作者：

Jackson, Joe ^{[1
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

ANNALS OF APPLIED PROBABILITY | 2024年 / 34卷 / 1A期

基金：

美国国家科学基金会;

关键词：

Quadratic FBSDE; quasilinear parabolic systems; Holder estimate; gradient estimate; STOCHASTIC DIFFERENTIAL-EQUATIONS; UNIQUENESS; EXISTENCE; GAMES;

D O I：

10.1214/23-AAP1966

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：

Using probabilistic methods, we establish a priori estimates for two classes of quasilinear parabolic systems of partial differential equations (PDEs). We treat in particular the case of a nonlinearity, which has quadratic growth in the gradient of the unknown. As a result of our estimates, we obtain the existence of classical solutions of the PDE system. From this, we infer the existence of solutions to a corresponding class of forward backward stochastic differential equations.

引用

页码：357 / 387

页数：31

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