Lectures on Probability Theory

This book contains work-outs of the notes of three 15-hour courses of lectures which constitute surveys on the concerned topics given at the St. Flour Probability Summer School in July 1992. The first course, by D. Bakry, is concerned with hypercontractivity properties and their use in semi-group theory, namely Sobolev and Log Sobolev inequalities, with estimations on the density of the semi-groups. The second one, by R.D. Gill, is about statistics on survival analysis; it includes product-integral theory, Kaplan-Meier estimators, and a look at cryptography and generation of randomness. The third one, by S.A. Molchanov, covers three aspects of random media: homogenization theory, localization properties and intermittency. Each of these chapters provides an introduction to and survey of its subject.