Semiclassical Analysis for Diffusions and Stochastic Processes PDF
by Vassili N. Kolokoltsov
Part of the Lecture Notes in Mathematics series
Description
The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Levy processes, (iii) complex stochastic Schrodinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus.
Information
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Download - Immediately Available
- Format:PDF
- Publisher:Springer Berlin Heidelberg
- Publication Date:03/12/2007
- Category:
- ISBN:9783540465874
Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Springer Berlin Heidelberg
- Publication Date:03/12/2007
- Category:
- ISBN:9783540465874
