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Functional inequalities on path spaces of processes with independent increments. (English. Russian original) Zbl 1253.60061

Russ. Math. Surv. 67, No. 2, 381-383 (2012); translation from Usp. Mat. Nauk 67, No. 2, 191-192 (2012).
This interesting research announcement contains a logarithmic Sobolev inequality and a Poincaré inequality for functionals of processes with independent increments. For this, the author uses the canonical representation of the process, the Clark-Ocone formula, and the chaos decomposition.

MSC:

60G51 Processes with independent increments; Lévy processes
60E15 Inequalities; stochastic orderings
60H07 Stochastic calculus of variations and the Malliavin calculus
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