Poincaré inequality and exponential integrability of hitting times for linear diffusions

2009/07/04 by Loukianova, D., Loukianov, O., Song, Sh.
#60J25 #60J35 #60J60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0907.0762

Abstract

Let X be a regular linear continuous positively recurrent Markov process with state space \R, scale function S and speed measure m. For a∈ \R denote B⁺_a&=sup_{x≥ a} \m(]x,+∞[)(S(x)-S(a)) B^-_a&=sup_{x≤ a} \m(]-∞;x[)(S(a)-S(x)) We study some characteristic relations between B⁺_a, B^-_a, the exponential moments of the hitting times T_a of X, the Hardy and Poincaré inequalities for the Dirichlet form associated with X. As a corollary, we establish the equivalence between the existence of exponential moments of the hitting times and the spectral gap of the generator of X.

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