Probability Theory, An Analytic View

Daniel W. Stroock

ISBN 10: 1009549006 / ISBN 13: 9781009549004

Editore: Cambridge University Press, GB, 2024

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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.

Codice articolo LU-9781009549004

Dati bibliografici

• Titolo: Probability Theory, An Analytic View
• Editore: Cambridge University Press, GB
• Data di pubblicazione: 2024
• Lingua: Inglese
• ISBN 10: 1009549006
• ISBN 13: 9781009549004
• Rilegatura: Paperback
• Edizione: terza edizione
• Condizione: New
• Dimensioni: 17,78 L x 2,39 A x 25,4 P centimetri 17,78 centimetri di larghezza per 2,39 centimetri di altezza per 25,4 centimetri di profondità
• Peso: 867 grammi

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Riassunto

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.