A Probabilistic Scheme for Fully Non-linear Non-local Parabolic PDEs with singular Levy measuresReportar como inadecuado




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1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

Abstract : 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 the scheme.
We consider the equations whose non-linearity is of the Hamilton-Jacobi-Belman type.
We avoid the difficulties of infinite Levy measures by truncation of the Levy integral by some $\kappa>0$ near $0$.
The first result provides the convergence of the scheme for general parabolic non-linearities.
The second result provides bounds on the rate of convergence for concave non-linearities from above and below.
For both results, it is crucial to choose $\kappa$ appropriately dependent on $h$.


keyword : Viscosity solution non-local PDE Monte Carlo approximation





Autor: Arash Fahim -

Fuente: https://hal.archives-ouvertes.fr/



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