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Hitting times and spectral gap inequalities. (English) Zbl 0894.60070
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 $$\mathbb{R}^n$$ 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:
 60J25 Continuous-time Markov processes on general state spaces 60J60 Diffusion processes
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