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arXiv · 1709.07743

On the rate of convergence for monotone numerical schemes for nonlocal Isaacs' equations

Imran H. Biswas·Indranil Chowdhury·Espen R. Jakobsen
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Abstract

We study monotone numerical schemes for nonlocal Isaacs equations, the dynamic programming equations of stochastic differential games with jump-diffusion state processes. These equations are fully-nonlinear non-convex equations of order less than $2$. In this paper they are also allowed to be degenerate and have non-smooth solutions. The main contribution is a series of new a priori error estimates: The first results for nonlocal Isaacs equations, the first general results for degenerate non-convex equations of order greater than $1$, and the first results in the viscosity solution setting giving the precise dependence on the fractional order of the equation. We also observe a new phenomena, that the rates differ when the nonlocal diffusion coefficient depend on $x$ and $t$, only on $x$, or on neither.

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Imran H. Biswas, Indranil Chowdhury, Espen R. Jakobsen. 2017-09-22. On the rate of convergence for monotone numerical schemes for nonlocal Isaacs' equations. https://arxiv.org/abs/1709.07743

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