Diffusions and Elliptic Operators (Paperback)

Richard F. Bass

ISBN 10: 1475771592 / ISBN 13: 9781475771596

Verlag: Springer-Verlag New York Inc., New York, NY, 2013

Beschreibung

Paperback. 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. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Bestandsnummer des Verkäufers 9781475771596

Bibliografische Details

• Titel: Diffusions and Elliptic Operators (Paperback)
• Verlag: Springer-Verlag New York Inc., New York, NY
• Erscheinungsjahr: 2013
• Sprache: Englisch
• ISBN-10: 1475771592
• ISBN-13: 9781475771596
• Einband: Paperback
• Zustand: new

Über diesen Titel

Inhaltsangabe

This book will serve as a reference book for graduate students and researchers in probability theory or partial differential equations who want to learn more about the interplay of these two areas.

Reseña del editor

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.