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arXiv · 1801.08794

Branching diffusion representation for nonlinear Cauchyproblems and Monte Carlo approximation

Pierre Henry-Labordere·Nizar Touzi
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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.

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Pierre Henry-Labordere, Nizar Touzi. 2018-01-26. Branching diffusion representation for nonlinear Cauchyproblems and Monte Carlo approximation. https://arxiv.org/abs/1801.08794

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