A modified \(\Phi \)-Sobolev inequality for canonical Lévy processes and its applications (Q6157632)

This paper proves a modified \(\Phi\)-Sobolev inequality for functionals of Brownian motion and pure jump Lévy processes, extending previous versions of this inequality that had been derived separately on the Wiener and Poisson spaces. As a consequence, concentration inequalities are derived using Lambert's \(W\)-function. Several application examples are presented using functionals of mixed Brownian motion and Poisson point processes, such as the running maximum of a Lévy process.