Large Deviations estimates for some non-local equations I. Fast decaying kernels and explicit bounds

TL;DR

This paper investigates large deviations for non-local parabolic equations, demonstrating exponential convergence rates to whole-space solutions depending on kernel decay, with explicit bounds derived for various kernel types.

Contribution

It provides explicit convergence rate estimates for non-local equations with different kernels, highlighting the impact of kernel decay on convergence.

Findings

Convergence to whole-space solutions occurs at an exponential rate.

Decay properties of kernels significantly influence convergence speed.

Explicit bounds are derived for various kernel examples.

Abstract

We study large deviations for some non-local parabolic type equations. We show that, under some assumptions on the non-local term, problems defined in a bounded domain converge with an exponential rate to the solution of the problem defined in the whole space. We compute this rate in different examples, with different kernels defining the non-local term, and it turns out that the estimate of convergence depends strongly on the decay at infinity of that kernel.