Semiclassical Analysis for Diffusions and Stochastic Processes

• Main Author: Kolokoltsov, Vassili N. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
• Edition: 1st ed. 2000.
• Series: Lecture Notes in Mathematics, 1724
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Probabilities.; Analysis.; Probability Theory and Stochastic Processes.

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-diffusio...

Table of 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.