Stochastic Processes And Boundary Value Problems
In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani's 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion. However, it turns out that for a large class of semi-elliptic second-order partial differential equations the associated Dirichlet boundary value problem can be solved using an Itō process that solves an associated stochastic differential equation.
Read more about Stochastic Processes And Boundary Value Problems: Introduction: Kakutani's Solution To The Classical Dirichlet Problem, The Dirichlet-Poisson Problem
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