Semiclassical Analysis for Diffusions and Stochastic Processes / by Vassili N. Kolokoltsov.

Format:

Book

Author/Creator:

Kolokolʹt︠s︡ov, V. N. (Vasiliĭ Nikitich), author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1724.

Lecture Notes in Mathematics, 0075-8434 ; 1724

Language:

English

Subjects (All):

Global analysis (Mathematics).

Distribution (Probability theory).

Analysis.

Probability Theory and Stochastic Processes.

Local Subjects:

Analysis.

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (VIII, 356 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.

System Details:

text file PDF

Summary:

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:

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-diffusions

Semiclassical asymptotics for the localised Feller-Courrège processes

Complex stochastic diffusion or stochastic Schrödinger equation

Some topics in semiclassical spectral analysis

Path integration for the Schrödinger, heat and complex diffusion equations.

Other Format:

Printed edition:

ISBN:

9783540465874

Access Restriction:

Restricted for use by site license.