Hyperfinite Dirichlet Forms and Stochastic Processes

Sergio Albeverio

ISBN 10: 3642196586 / ISBN 13: 9783642196584

Published by Springer Berlin Heidelberg, 2011

About this Item

Druck auf Anfrage Neuware - Printed after ordering - This monograph treats the theory of Dirichlet forms from a comprehensive point of view, using 'nonstandard analysis.' Thus, it is close in spirit to the discrete classical formulation of Dirichlet space theory by Beurling and Deny (1958). The discrete infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same methods. This setting has the advantage of being independent of special topological properties of the state space and in this sense is a natural one, valid for both finite- and infinite-dimensional spaces. The present monograph provides a thorough treatment of the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes, and summarizes in an epilogue the model-theoretic genericity of hyperfinite stochastic processes theory.

Seller Inventory # 9783642196584

Bibliographic Details

• Title: Hyperfinite Dirichlet Forms and Stochastic Processes
• Publisher: Springer Berlin Heidelberg
• Publication Date: 2011
• Language: English
• ISBN 10: 3642196586
• ISBN 13: 9783642196584
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 17D millimeters 235 millimeters width by 155 millimeters height by 17 millimeters depth
• Weight: 458 grams

About this title

Synopsis

This monograph treats the theory of Dirichlet forms from a comprehensive point of view, using "nonstandard analysis." Thus, it is close in spirit to the discrete classical formulation of Dirichlet space theory by Beurling and Deny (1958). The discrete infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same methods. This setting has the advantage of being independent of special topological properties of the state space and in this sense is a natural one, valid for both finite- and infinite-dimensional spaces.

The present monograph provides a thorough treatment of the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes, and summarizes in an epilogue the model-theoretic genericity of hyperfinite stochastic processes theory.