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Zbl 0894.60070
Mathieu, P.
Hitting times and spectral gap inequalities. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 33, No.4, 437-465 (1997). ISSN 0246-0203

Summary: The aim of this paper is to relate estimates on the hitting times of closed sets by a Markov process and a special class of inequalities involving the $L_p$ $(p\leq 1)$ norm of a function and its Dirichlet norm. These inequalities are weaker than the usual spectral gap inequality. In particular they hold for diffusion processes in $\bbfR^n$ when the potential decreases polynomially. We derive uniform bounds for the moments of the hitting times. We also obtain estimates of the difference between the law of the hitting time of a ``small'' set and an exponential law.

MSC 2000:: *60J25 Markov processes with continuous parameter
60J60 Diffusion processes

Keywords: Markov process; inequalities; Dirichlet norm; hitting times; exponential law

Cited in: Zbl 1249.60167 Zbl pre05908023 Zbl 1018.82019

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