Semiclassical Analysis for Diffusions and Stochastic Processes

Vassili N. Kolokoltsov

346 pages, parution le 15/04/2000

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Résumé

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 Lévy processes, (iii) complex stochastic Schrödinger 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.

Contents

Introduction

Gaussian diffusions
Boundary value problem for Hamiltonian systems
Semiclassical approximation for regular diffusion
Invariant degenerate diffusion on cotangent bundles
Transition probability densities for stable-jump-diffusion
Semiclassical asymptotics for the localized Feller-Courrège processes
Complex stochastic diffusions or stochastic Schrödinger equations
Some topics in semiclassical spectral analysis
Path integration for the Schrödinger, heat and complex stochastic diffusion equations

Appendices
References
Main notations
Subject Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Vassili N. Kolokoltsov
Parution	15/04/2000
Nb. de pages	346
Format	15,5 x 23,5
Couverture	Broché
Poids	472g
Intérieur	Noir et Blanc
EAN13	9783540669722