Monte Carlo for high-dimensional degenerated Semi Linear and Full Non Linear PDEs

2018/05/14 by Xavier Warin, Warin, Xavier
Mathematics · #65C05 49L25 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:49L25 #msc:65C05

paper · pdf · doi:10.48550/arxiv.1805.05078

23 pages, 13 figures

arxiv created 2018/05/14 · arxiv updated 2018/05/15

Abstract

We extend a recently developed method to solve semi-linear PDEs to the case of a degenerated diffusion. Being a pure Monte Carlo method it does not suffer from the so called curse of dimensionality and it can be used to solve problems that were out of reach so far. We give some results of convergence and show numerically that it is effective. Besides we numerically show that the new scheme developed can be used to solve some full non linear PDEs. At last we provide an effective algorithm to implement the scheme.

Related

• Nesting Monte Carlo for high-dimensional Non Linear PDEs
• Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
• Branching diffusion representation of semi-linear elliptic PDEs and estimation using Monte Carlo method
• Branching diffusion representation for nonlinear Cauchyproblems and Monte Carlo approximation
• An iterative Monte Carlo method to solve nonlinear second-order differential equations