Hyperfinite Dirichlet Forms and Stochastic Processes
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Beschreibung
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.
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.
Includes historical notes and comprehensive bibliography An appendix on nonstandard analysis makes the book self-contained A special chapter on Lévy processes increases the scope of applications Includes supplementary material: sn.pub/extras
Autor*in
Sergio Albeverio
Themen in »Hyperfinite Dirichlet Forms and Stochastic Processes«
03H05 60J45 Dirichlet form Markov processes non-standard analysis
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From the reviews:
“This book deals with the relationship between Dirichlet forms and stochastic processes from the perspective of nonstandard analysis. … The book has a very extensive bibliography and gives an interesting and valuable survey of the development and the applications of the theory of Dirichlet forms. … the book will serve as a starting point for new explorations.” (Tom L. Lindström, Mathematical Reviews, Issue 2012 k)
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