HYPER FINITE DIRICHLET FORMS AND STOCHASTIC PROCESSES
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- Author: FREDERIK HERZBERG
- ISBN: 9783642196584
- Availability: In Stock
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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.