Higher order asymptotics for large deviations -- Part II
We obtain asymptotic expansions for the large deviation principle (LDP) for continuous time stochastic processes with weakly dependent increments. As a key example, we show that additive functionals of solutions of stochastic differential equations (SDEs) satisfying H\"ormander condition on a $d-$dimensional compact manifold admit these asymptotic expansions of all orders.
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Phillip Griffiths Assistant Research Professor
I am a Griffiths Assistant Research Professor at the Department of Mathematics at Duke University. Prior to arriving at Duke, I completed my Ph.D. from the Department of Mathematics at the University of Maryland. The main focus of my research is asymptotic problems arising from Branching Processes, Branching Diffusions and related Dynamical Systems.