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2013•arXiv (Cornell University)Open access

Poincare inequality and exponential integrability of the hitting times\n of a Markov process

Alexei Kulik

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Abstract

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

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

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Available abstract

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

Key concepts: Poincaré conjecture, Poincaré inequality, Hitting time, Mathematics, Spectral gap, Exponential function, Markov process, Inequality

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