Convergence of a Monte Carlo Method for Fully Non-linear Elliptic and Parabolic Pdes in Some General Domains
نویسنده
چکیده
In this paper, we introduce a probabilistic numerical scheme for a class of parabolic and elliptic fully non-linear PDEs in bounded domains. In the main result, we provide the convergence of a discrete-time approximation to the viscosity solution of a fully non-linear parabolic equation by assuming that comparison principle holds for the PDE.
منابع مشابه
A Probabilistic Scheme for Fully Non-linear Non-local Parabolic Pdes with Singular Lévy Measures
We introduce a Monte Carlo scheme for the approximation of the solutions of fully non–linear parabolic non–local PDEs. The method is the generalization of the method proposed by [Fahim-Touzi-Warin, 2011] for fully non–linear parabolic PDEs. As an independent result, we also introduce a Monte Carlo Quadrature method to approximate the integral with respect to Lévy measure which may appear inside...
متن کاملMulti-level Higher Order Qmc Galerkin Discretization for Affine Parametric Operator Equations
We develop a convergence analysis of a multi-level algorithm combining higher order quasi-Monte Carlo (QMC) quadratures with general Petrov-Galerkin discretizations of countably affine parametric operator equations of elliptic and parabolic type, extending both the multi-level first order analysis in [F.Y. Kuo, Ch. Schwab, and I.H. Sloan, Multi-level quasi-Monte Carlo finite element methods for...
متن کاملFurther analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients
We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and that only have limited spatial regularity. We extend the finite element error analysis for this type of equation, carried out in [6], to more difficult problem...
متن کاملA MIXED PARABOLIC WITH A NON-LOCAL AND GLOBAL LINEAR CONDITIONS
Krein [1] mentioned that for each PD equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. They claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. They have only considered lo...
متن کاملFeynman-Kac representation of fully nonlinear PDEs and applications
The classical Feynman-Kac formula states the connection between linear parabolic partial differential equations (PDEs), like the heat equation, and expectation of stochastic processes driven by Brownian motion. It gives then a method for solving linear PDEs by Monte Carlo simulations of random processes. The extension to (fully)nonlinear PDEs led in the recent years to important developments in...
متن کامل