Lectures on Probability Theory
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Author Description
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. The third one, by S.A. Molchanov, covers three aspects of random media: homogenization theory, loca- lization properties and intermittency. Each of these chap- ters provides an introduction to and survey of its subject.
Menrva's Summary
THE THESIS
This volume presents advanced lectures on key topics in probability theory, delivered at the 1992 Saint-Flour Probability Summer School. The book comprises three distinct courses, each offering a comprehensive survey of its respective field. D. Bakry's lectures explore hypercontractivity properties and their applications in semi-group theory, including Sobolev and Log Sobolev inequalities. R.D. Gill's contribution focuses on statistical methods in survival analysis, detailing product-integral theory and Kaplan-Meier estimators. S.A. Molchanov's work delves into the theory of random media, covering homogenization, localization, and intermittency.
THE SCOPE MAP
- Introduction to hypercontractivity properties and their use in semi-group theory.
- Detailed examination of Sobolev and Log Sobolev inequalities with estimations on semi-group densities.
- Survey of statistics in survival analysis, including product-integral theory.
- Exploration of Kaplan-Meier estimators and their applications.
- Coverage of cryptography and the generation of randomness within statistical contexts.
- Introduction to homogenization theory in random media.
- Discussion of localization properties in random media.
- Analysis of intermittency phenomena in random media.
THE AUTHORITY PERSPECTIVE
This collection of lectures is structured to provide an introduction and survey of specialized topics within probability theory and its applications. The content is likely to appeal to researchers and advanced students in mathematics and statistics seeking to deepen their understanding of semi-group theory, survival analysis, and random media. The detailed notes from intensive courses suggest a rigorous and comprehensive treatment of each subject area.
Page Count:
419
Publication Date:
1994-01-01
ISBN-10:
0387582088
ISBN-13:
9780387582085
Non-Fiction
Nature
Science
Statistics
Stochastic processes
Probability Theory
Mathematical Analysis
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