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Martingales, Poincaré Type Inequalities, and Deviation Inequalities

✍ Scribed by Michael Schmuckenschläger

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
354 KB
Volume
155
Category
Article
ISSN
0022-1236

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✦ Synopsis

Using martingale techniques we will prove several deviation inequalities for diffusion processes in a compact Riemannian manifold and Le vy processes in euclidean space. We also deduce deviation inequalities from Poincare type inequalities in the abstract setting of Dirichlet forms. We thus obtain, in a unified way, the theorems of Alon Milman, Gromov Milman, and a deviation inequality for the Laplace disribution.

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