Semiclassical analysis for diffusions 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-diffusi...
| Main Author: | |
|---|---|
| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer,
[2000]
|
| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1724. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| 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 Lvy processes, (iii) complex stochastic Schrdinger 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. |
|---|---|
| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (viii, 345 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages [329]-345) and index. |
| ISBN: | 9783540465874 (electronic bk.) 3540465871 (electronic bk.) |
| ISSN: | 0075-8434 ; |