Modern survival analysis and more general event history analysis may be effectively handled in the mathematical framework of counting processes, stochastic integration, martingale central limit theory and product integration. This book presents this theory, which has been the subject of an intense research activity during the past one-and-a- half decades. The exposition of the theory is integrated with careful presentation of many practical examples, almost exclusively from the authors' own experience, with detailed numerical and graphical illustrations. Statistical Models Based on Counting...

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 inequa- lities, with estimations on the density of the semi-groups. The second one, by R.D. Gill, is about statistics on survi- val analysis; it includes product-integral theory, Kaplan- Meier estimators, and a look at cryptography and generation of randomness....