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arXiv · 0909.1467

Large Deviations estimates for some non-local equations. General bounds and applications

Cristina Brändle·Emmanuel Chasseigne
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Abstract

Large deviation estimates for the following linear parabolic equation are studied: \[ \frac{\partial u}{\partial t}=\tr\Big(a(x)D^2u\Big) + b(x)\cdot D u + \int_{\R^N} \Big\{(u(x+y)-u(x)-(D u(x)\cdot y)\ind{|y|<1}(y)\Big\}\dμ(y), \] where $μ$ is a Lévy measure (which may be singular at the origin). Assuming only that some negative exponential integrates with respect to the tail of $μ$, it is shown that given an initial data, solutions defined in a bounded domain converge exponentially fast to the solution of the problem defined in the whole space. The exact rate, which depends strongly on the decay of $μ$ at infinity, is also estimated.

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Cristina Brändle, Emmanuel Chasseigne. 2009-09-08. Large Deviations estimates for some non-local equations. General bounds and applications. https://arxiv.org/abs/0909.1467

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