Diffusions and Elliptic Operators

Richard F. Bass

ISBN 10: 0387983155 / ISBN 13: 9780387983158

Editore: Springer New York, Springer New York, 1997

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Druck auf Anfrage Neuware - Printed after ordering - This is author-approved bcc: This book discusses the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods in PDE. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE. After spending three chapters on probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions, the author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators. Martingale problems and the Malliavin calculus are presented in two other chapters. This book can be used as a textbook for a graduate course on diffusion theory with applications to PDE. It will also be a valuable reference to researchers in probability who are interested in PDE as well as for analysts who are interested in probabilistic methods.

Codice articolo 9780387983158

Dati bibliografici

• Titolo: Diffusions and Elliptic Operators
• Editore: Springer New York, Springer New York
• Data di pubblicazione: 1997
• Lingua: Inglese
• ISBN 10: 0387983155
• ISBN 13: 9780387983158
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 19 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 19 millimetri di profondità
• Peso: 547 grammi

Descrizione articolo

Riassunto

A discussion of the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE, and moves on to probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions. The author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators, as well as Martingale problems and the Malliavin calculus. While serving as a textbook for a graduate course on diffusion theory with applications to PDE, this will also be a valuable reference to researchers in probability who are interested in PDE, as well as for analysts interested in probabilistic methods.

Contenuti

Stochastic Differential Equations.- Representations of Solutions.- Regularity of Solutions.- One-dimensional Diffusions.- Nondivergence form Operators.- Martingale Problems.- Divergence Form Operators.- The Malliavin Calculus.