Abakirova, A. T. 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. Reviewer: Michael Voit (Dortmund) Cited in 1 Document MSC: 60G51 Processes with independent increments; Lévy processes 60E15 Inequalities; stochastic orderings 60H07 Stochastic calculus of variations and the Malliavin calculus Keywords:logarithmic Sobolev inequality; Poincaré inequality; processes with independent increments PDFBibTeX XMLCite \textit{A. T. Abakirova}, Russ. Math. Surv. 67, No. 2, 381--383 (2012; Zbl 1253.60061); translation from Usp. Mat. Nauk 67, No. 2, 191--192 (2012) Full Text: DOI