Abstract.
By means of the martingale representation, we establish a new modified logarithmic Sobolev inequality, which covers the previous modified logarithmic Sobolev inequalities of Bobkov-Ledoux and the L 1-logarithmic Sobolev inequality obtained in our previous work. From it we derive several sharp deviation inequalities of Talagrand's type, by following the powerful Herbst method developed recently by Ledoux and al. Moreover this new modified logarithmic Sobolev inequality is transported on the discontinuous path space with respect to the law of a Lévy process.
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Received: 16 June 1999 / Revised version: 13 March 2000 / Published online: 12 October 2000
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Wu, L. A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probab Theory Relat Fields 118, 427–438 (2000). https://doi.org/10.1007/PL00008749
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DOI: https://doi.org/10.1007/PL00008749
Keywords
- Point Process
- Sobolev Inequality
- Poisson Point Process
- Path Space
- Sharp Deviation