Branching diffusion representation for nonlinear Cauchyproblems and Monte Carlo approximation
Probability
2018-01-29 v1 Mathematical Physics
Analysis of PDEs
math.MP
Numerical Analysis
Abstract
We provide a probabilistic representations of the solution of some semilinear hyperbolicand high-order PDEs based on branching diffusions. These representations pave theway for a Monte-Carlo approximation of the solution, thus bypassing the curse ofdimensionality. We illustrate the numerical implications in the context of some popularPDEs in physics such as nonlinear Klein-Gordon equation, a simplied scalar versionof the Yang-Mills equation, a fourth-order nonlinear beam equation and the Gross-Pitaevskii PDEas an example of nonlinear Schrodinger equations.
Cite
@article{arxiv.1801.08794,
title = {Branching diffusion representation for nonlinear Cauchyproblems and Monte Carlo approximation},
author = {Pierre Henry-Labordere and Nizar Touzi},
journal= {arXiv preprint arXiv:1801.08794},
year = {2018}
}