Inégalités isopérimétriques et calcul stochastique. (Isoperimetric inequalities and stochastic calculus). (French) Zbl 0649.60003

Ledoux, Michel

Séminaire de probabilités XXII, Strasbourg/France, Lect. Notes Math. 1321, 249-259 (1988).

[For the entire collection see Zbl 0635.00013.]
This expository note presents an argument of B. Maurey that uses stochastic calculus and Itô’s formula for Brownian motion to derive concentration inequalities of isoperimetric type for Gaussian measures. The paper briefly presents as well some classical consequences and applications to integrability and tail behavior properties of suprema of Gaussian processes and of Gaussian chaos.

Reviewer: M.Ledoux

MSC:

60B05	Probability measures on topological spaces
60H05	Stochastic integrals
60E15	Inequalities; stochastic orderings
60G15	Gaussian processes

Keywords:

expository note; stochastic calculus; Itô’s formula; concentration inequalities of isoperimetric type for Gaussian measures; Gaussian processes; Gaussian chaos

Citations:

Zbl 0635.00013