ON QUASILINEAR PARABOLIC SYSTEMS AND FBSDES OF QUADRATIC GROWTH

• 成果类型: Article
• 署名作者: Jackson, Joe
• 署名单位: University of Texas System; University of Texas Austin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1966
• 发表日期: 2024
• 页码: 357-387
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; uniqueness; EXISTENCE; games

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.