Branching diffusion representation for nonlinear Cauchy problems and Monte Carlo approximation

DOI10.1214/20-AAP1649zbMath1476.35090arXiv1801.08794OpenAlexW3208281062MaRDI QIDQ2240887

Nizar Touzi, Pierre Henry-Labordère

Publication date: 4 November 2021

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.08794

zbMATH Keywords

branching processesGross-Pitaevskii equationnonlinear Klein-Gordon equationYang-Mills equationDuhamel formulafourth-order nonlinear beam equation

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Applications of branching processes (60J85) Integral representations of solutions to PDEs (35C15) Initial value problems for nonlinear higher-order PDEs (35G25)

Related Items (5)

An Unbiased Itô Type Stochastic Representation for Transport PDEs: A Toy Example ⋮ Existence and probabilistic representation of the solutions of semilinear parabolic PDEs with fractional Laplacians ⋮ XVA in a multi-currency setting with stochastic foreign exchange rates ⋮ A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders ⋮ A deep branching solver for fully nonlinear partial differential equations

Cites Work

• Unnamed Item
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• A probabilistic numerical method for fully nonlinear parabolic PDEs
• Monte Carlo solution of Cauchy problem for a nonlinear parabolic equation
• A stochastic model related to the telegrapher's equation
• Stochastic cascades and 3-dimensional Navier-Stokes equations
• A numerical scheme for BSDEs
• Numerical approximation of BSDEs using local polynomial drivers and branching processes
• Unbiased simulation of stochastic differential equations
• Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
• Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
• Branching diffusion representation of semi-linear elliptic PDEs and estimation using Monte Carlo method
• Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions
• A numerical algorithm for a class of BSDEs via the branching process
• Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
• Error analysis of the optimal quantization algorithm for obstacle problems.
• Solutions of semilinear wave equation via stochastic cascades
• A Feynman-Kac-type formula for the deterministic and stochastic wave equations and other p.d.e.'s
• Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov

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