Large deviation estimates for some nonlocal equations. General bounds and applications
Cristina Brändle, Emmanuel Chasseigne · Transactions of the American Mathematical Society · 2013
Large deviation estimates for the following linear parabolic equation are studied: \[ ∂ u ∂ t = Tr ( a ( x ) D 2 u ) + b ( x ) ⋅ D u + L [ u ] ( x ) , \frac {\partial u}{\partial t}=\textrm {Tr}\Big ( a(x)D^2u\Big ) + b(x)\cdot D u+ \mathcal {L}[u](x), \] where L [ u ] \mathcal {L}[u] is a nonlocal Lévy-type term associated to a Lévy measure μ \mu (which may be singular at the origin): \[ L [ u ] ( x ) = ∫ R N { ( u ( x + y ) − u ( x ) − ( D u ( x ) ⋅ y ) 1 I