Multidimensional viscosity solutions theory of semi-linear partial differential equations
Shuzhen Yang
TL;DR
This paper develops a new multidimensional viscosity solutions framework for semi-linear PDEs, linking it to multidimensional BSDEs, and proves existence and uniqueness results using comparison theorems and approximation methods.
Contribution
It introduces a novel definition of viscosity solutions for multidimensional semi-linear PDEs connected to BSDEs, and establishes foundational existence and uniqueness results.
Findings
New definition of multidimensional viscosity solutions
Existence and uniqueness of solutions proven
Connection established between PDEs and BSDEs
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and financial applications · Nonlinear Differential Equations Analysis · Stochastic processes and statistical mechanics