Maximum Principle for Quasilinear Stochastic PDEs with Obstacle
Denis Laurent, Matoussi Anis, Zhang Jing
TL;DR
This paper establishes a maximum principle for local solutions of quasilinear stochastic PDEs with obstacle, utilizing Itô's formula and boundary estimates to handle the stochastic and obstacle constraints.
Contribution
It introduces a maximum principle for OSPDEs, extending classical PDE results to stochastic equations with obstacles using novel probabilistic techniques.
Findings
Maximum principle proven for local solutions of OSPDEs
Utilizes Itô's formula for stochastic analysis
Provides boundary estimates for solutions
Abstract
We prove a maximum principle for local solutions of quasilinear stochastic PDEs with obstacle (in short OSPDE). The proofs are based on a version of It\^o's formula and estimates for the positive part of a local solution which is non-positive on the lateral boundary.
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Taxonomy
TopicsStochastic processes and financial applications · Economic theories and models · Insurance, Mortality, Demography, Risk Management