Φ-entropy inequality and application for SDEs with jumps

By using the Φ-entropy inequality derived in [16,2] for Poisson measures, the same type of inequality is established for a class of stochastic differential equations driven by purely jump Lévy processes. This inequality implies the exponential convergence in Φ-entropy of the associated Markov semigroup. The semigroup Φ-entropy inequality for SDEs driven by Poisson point processes is also considered.