Difference-quadrature schemes for nonlinear degenerate parabolic integro-PDE
Analysis of PDEs
2009-06-09 v1 Numerical Analysis
Abstract
We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Levy (jump-diffusion) processes. These equations are fully non-linear, degenerate parabolic integro-PDEs interpreted in the sense of viscosity solutions. We propose new ``direct'' discretizations of the non-local part of the equation that give rise to monotone schemes capable of handling singular Levy measures. Furthermore, we develop a new general theory for deriving error estimates for approximate solutions of integro-PDEs, which thereafter is applied to the proposed difference-quadrature schemes.
Keywords
Cite
@article{arxiv.0906.1458,
title = {Difference-quadrature schemes for nonlinear degenerate parabolic integro-PDE},
author = {I. H. Biswas and E. R. Jakobsen and K. H. Karlsen},
journal= {arXiv preprint arXiv:0906.1458},
year = {2009}
}