Semiclassical Analysis for Diffusions and Stochastic Processes

Vassili N. Kolokoltsov (Autor)

Buch | Softcover

VIII, 356 Seiten

2000
Springer Berlin (Verlag)
9783540669722 (ISBN)

Artikel merken

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.

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.

Erscheint lt. Verlag	27.3.2000
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	VIII, 356 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	468 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Boundary value problem • Diffusion • Hardcover, Softcover / Mathematik/Analysis • HC/Mathematik/Analysis • Lévy process • Markov process • Markov Processes • path integral • semiclassical approximation • Stochastic Hamilton-Jacobi and Schröder equations • Stochastic process • Stochastic Processes • Stochastischer Prozess • Stochastischer Prozeß
ISBN-13	9783540669722 / 9783540669722
Zustand	Neuware