Probability Theory, An Analytic View

Daniel W. Stroock

ISBN 10: 1009549006 / ISBN 13: 9781009549004

Edité par Cambridge University Press, GB, 2024

A propos de cet article

The third edition of this highly regarded text provides a rigorous, yet entertaining, introduction to probability theory and the analytic ideas and tools on which the modern theory relies. The main changes are the inclusion of the Gaussian isoperimetric inequality plus many improvements and clarifications throughout the text. With more than 750 exercises, it is ideal for first-year graduate students with a good grasp of undergraduate probability theory and analysis. Starting with results about independent random variables, the author introduces weak convergence of measures and its application to the central limit theorem, and infinitely divisible laws and their associated stochastic processes. Conditional expectation and martingales follow before the context shifts to infinite dimensions, where Gaussian measures and weak convergence of measures are studied. The remainder is devoted to the mutually beneficial connection between probability theory and partial differential equations, culminating in an explanation of the relationship of Brownian motion to classical potential theory.

N° de réf. du vendeur LU-9781009549004

Détails bibliographiques

• Titre: Probability Theory, An Analytic View
• Éditeur: Cambridge University Press, GB
• Date de parution: 2024
• Langue: anglais
• ISBN à 10 chiffres: 1009549006
• ISBN à 13 chiffres: 9781009549004
• Reliure: Paperback
• Édition: 3ème Édition
• État de l'article: New

A propos de ce titre

Synopsis

The third edition of this highly regarded text provides a rigorous, yet entertaining, introduction to probability theory and the analytic ideas and tools on which the modern theory relies. The main changes are the inclusion of the Gaussian isoperimetric inequality plus many improvements and clarifications throughout the text. With more than 750 exercises, it is ideal for first-year graduate students with a good grasp of undergraduate probability theory and analysis. Starting with results about independent random variables, the author introduces weak convergence of measures and its application to the central limit theorem, and infinitely divisible laws and their associated stochastic processes. Conditional expectation and martingales follow before the context shifts to infinite dimensions, where Gaussian measures and weak convergence of measures are studied. The remainder is devoted to the mutually beneficial connection between probability theory and partial differential equations, culminating in an explanation of the relationship of Brownian motion to classical potential theory.

À propos de l?auteur

Daniel W. Stroock is Simons Professor Emeritus of Mathematics at the Massachusetts Institute of Technology. He has published numerous articles and books, most recently 'Elements of Stochastic Calculus and Analysis' (2018) and 'Gaussian Measures in Finite and Infinite Dimensions' (2023).