Nash Inequalities for Markov Processes in Dimension One |
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| Authors: | Young Hua Mao |
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| Institution: | (1) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China E-mail: yonghuamao@263.net, CN |
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| Abstract: | In this paper, we give characterizations of Nash inequalities for birth-death process and diffusion process on the line.
As a by-product, we prove that for these processes, transience implies that the semigroups P(t) decay as
∥P(t)∥1→∞≥Ct
−1.
Sufficient conditions for general Markov chains are also obtained.
Received November 29, 2000, Revised February 21, 2001, Accepted March 16, 2001 |
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| Keywords: | Nash inequalities Hardy type inequality Birth-death process Diffusion |
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