Poincare inequality and exponential integrability of the hitting times of a Markov process
Abstract
Extending the approach of the paper [Mathieu, P. (1997) Hitting times and spectral gap inequalities, Ann. Inst. Henri Poincare 33, 4, 437  465], we prove that the Poincare inequality for a (possibly nonsymmetric) Markov process yields the exponential integrability of the hitting times of this process. For symmetric elliptic diffusions, this provides a criterion for the Poincare inequality in the terms of hitting times.
 Publication:

arXiv eprints
 Pub Date:
 March 2013
 arXiv:
 arXiv:1303.1257
 Bibcode:
 2013arXiv1303.1257K
 Keywords:

 Mathematics  Probability
 EPrint:
 A.M.Kulik, Poincare inequality and exponential integrability of the hitting times of a Markov process, Theory of Stoch. Proc. vol. 17(33), 2011, no. 2, 71  80