A new modified logarithmic Sobolev inequality for Poisson point processes and several applications

• DOI: 10.1007/pl00008749
• Publication Date: 2006-04-10T11:05:32Z
• Authors: Liming Wu
• Keywords: 0101 mathematics; 01 natural sciences

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 Levy process.