Transportation inequalities for stochastic differential equations of pure jumps

Abstract

For stochastic differential equations of pure jumps, though the Poincaré inequality does not hold in general, we show that W1H transportation inequalities hold for its invariant probability measure and for its process-level law on right continuous paths space in the L 1-metric or in uniform metrics, under the dissipative condition. Several applications to concentration inequalities are given. © Association des Publications de l'Institut Henri Poincaré, 2010.