Multidimensional viscosity solutions theory of semi-linear partial differential equations

2016/08/07 by Shuzhen Yang, Yang, Shuzhen
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.AP #math.DS

paper · pdf · doi:10.48550/arxiv.1608.02204

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arxiv created 2016/08/07 · openalex publication_date 2016/08/07 · arxiv updated 2016/08/09 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28

Abstract

In this study, we concern the multidimensional viscosity solutions theory of a kind of semi-linear partial differential equations (PDEs). A new definition of viscosity solution for this multidimensional semi-linear PDEs which is related to a type of multidimensional backward stochastic differential equations (BSDEs) is given. Further more, we establish the existence and uniqueness results for the viscosity solution of this semi-linear PDEs via the comparison theorem of the related BSDEs and a smooth approximation technique.

Citations

• Conjugate convex functions in optimal stochastic control
• User’s guide to viscosity solutions of second order partial differential equations

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