Geodesic
Poincar\'e inequality and exponential integrability of the hitting times of a Markov process
Teoriâ slučajnyh processov, Tome 17 (2011) no. 2, pp. 71-80

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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.
Keywords: Markov process, exponential $\phi$-coupling, Poincaré inequality, hitting time. 
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     author = {Alexey M. Kulik},
     title = {Poincar\'e inequality and exponential integrability of the hitting times of a {Markov} process},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {71--80},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2011_17_2_a5/}
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Alexey M. Kulik. Poincar\'e inequality and exponential integrability of the hitting times of a Markov process. Teoriâ slučajnyh processov, Tome 17 (2011) no. 2, pp. 71-80. http://geodesic.mathdoc.fr/item/THSP_2011_17_2_a5/