Hyperfinite Dirichlet Forms and Stochastic Processes (Lecture Notes of the Unione Matematica Italiana, Vol. 10)

Albeverio, Sergio; Fan, Ruzong; Herzberg, Frederik S.

ISBN 10: 3642196586 / ISBN 13: 9783642196584

Edité par Springer, 2011

In. N° de réf. du vendeur ria9783642196584_new

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.

Présentation de l'éditeur: 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.

Détails bibliographiques

Titre : Hyperfinite Dirichlet Forms and Stochastic ...
Éditeur : Springer
Date d'édition : 2011
Reliure : Couverture souple
Etat : New