Poincaré inequality and exponential integrability of the hitting times of a Markov process

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