Semiclassical analysis for diffusions and stochastic processes:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2000
|
| Series: | Lecture notes in mathematics
1724 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [329] - 345 |
| Physical Description: | VIII, 345 S. |
| ISBN: | 3540669728 |
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| 100 | 1 | |a Kolokol'cov, Vassilij N. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Semiclassical analysis for diffusions and stochastic processes |c Vassili N. Kolokoltsov |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2000 | |
| 300 | |a VIII, 345 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1724 | |
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Record in the Search Index
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| adam_text | CONTENTS
Introduction 1
Chapter 1. Gaussian diffusions
1. Gaussian diffusion. Probabilistic and analytic approaches 17
2. Classification of Gaussian diffusions by the Young schemes 20
3. Long time behaviour of the Green functions of Gaussian diffusions 25
4. Complex stochastic Gaussian diffusion 28
5. The rate of escape for Gaussian diffusions
and scattering for its perturbations 34
Chapter 2. Boundary value problem for Hamiltonian systems
1. Rapid course in calculus of variations 40
2. Boundary value problem for non degenerate Hamiltonians 50
3. Regular degenerate Hamiltonians of the first rank 59
4. General regular Hamiltonians depending quadratically on momenta 72
5. Hamiltonians of exponential growth in momenta 75
6. Complex Hamiltonians and calculus of variations of saddle points 87
7. Stochastic Hamiltonians 92
Chapter 3. Semiclassical approximation for regular diffusion
1. Main ideas of the WKB method with imaginary phase 97
2. Calculation of the two point function for regular Hamiltonians 104
3. Asymptotic solutions of the transport equation 110
4. Local asymptotics of the Green function for regular Hamiltonians 112
5. Global small diffusion asymptotics and large deviations 119
6. Asymptotics for non regular diffusion: an example 124
7. Analytic solutions to some linear PDE 128
Chapter 4. Invariant degenerate diffusion on cotangent bundles
1. Curvilinear Ornstein Uhlenbeck process and stochastic geodesic flow. .. 136
2. Small time asymptotics for stochastic geodesic flow 140
3. The trace of the Green function and geometric invariants 143
Chapter 5. Transition probability densities for stable jump diffusion
1. Asymptotic properties of one dimensional stable laws 146
2. Asymptotic properties of finite dimensional stable laws 149
3. Transition probability densities for stable jump diffusion 161
4. Stable jump diffusions combined with compound Poisson processes 178
5. Stable like processes 182
6. Applications to the sample path properties of stable jump diffusions. ... 187
VIII
Chapter 6. Semiclassical asymptotics for the localised
Feller Courrege processes
1. Maslov s tunnel equations and the Feller Courrege processes 191
2. Rough local asymptotics and local large deviations 194
3. Refinement and globalisation 217
Chapter 7. Complex stochastic diffusions
or stochastic Schrodinger equations
1. Semiclassical approximation: formal asymptotics 223
2. Semiclassical approximation: justification and globalisation 229
3. Applications: two sided estimates to complex heat kernels,
large deviation principle, well posedness of the Cauchy problem 235
4. Path integration and infinite dimensional saddle point method 236
Chapter 8. Some topics in semiclassical spectral analysis
1. Double well splitting 239
2. Low lying eigenvalues of diffusion operators and the life times
of diffusion processes 247
3. Quasi modes of diffusion operators around a closed orbit
of the corresponding classical system 252
Chapter 9. Path integration for the Schrodinger, heat
and complex stochastic diffusion equations
1. Introduction 255
2. Path integral for the Schrodinger equation in p representation 263
3. Path integral for the Schrodinger equation in ^ representation 267
4. Singular potentials 269
5. Semiclassical asymptotics 272
6. Fock space representation 276
Appendices
A. Main equation of the theory of continuous quantum measurements 280
B. Asymptotics of Laplace integrals with complex phase 283
C. Characteristic functions of stable laws 293
D. Levy Khintchine ^DO and Feller Courrege processes 298
E. Equivalence of convex functions 303
F. Unimodality of symmetric stable laws 305
G. Infinite divisible complex distributions and complex Markov processes. 312
H. A review of main approaches to the rigorous construction
of path integral 322
I. Perspectives and problems 326
References 329
Main notations 346
Subject Index 347
|
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| indexdate | 2024-07-09T18:37:50Z |
| institution | BVB |
| isbn | 3540669728 |
| language | English |
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| physical | VIII, 345 S. |
| publishDate | 2000 |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Kolokol'cov, Vassilij N. Verfasser aut Semiclassical analysis for diffusions and stochastic processes Vassili N. Kolokoltsov Berlin [u.a.] Springer 2000 VIII, 345 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1724 Literaturverz. S. [329] - 345 Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Quasiklassische Näherung (DE-588)4296820-3 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Quasiklassische Näherung (DE-588)4296820-3 s DE-604 Diffusionsprozess (DE-588)4274463-5 s Lecture notes in mathematics 1724 (DE-604)BV000676446 1724 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008872691&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kolokol'cov, Vassilij N. Semiclassical analysis for diffusions and stochastic processes Lecture notes in mathematics Diffusionsprozess (DE-588)4274463-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Quasiklassische Näherung (DE-588)4296820-3 gnd |
| subject_GND | (DE-588)4274463-5 (DE-588)4057630-9 (DE-588)4296820-3 |
| title | Semiclassical analysis for diffusions and stochastic processes |
| title_auth | Semiclassical analysis for diffusions and stochastic processes |
| title_exact_search | Semiclassical analysis for diffusions and stochastic processes |
| title_full | Semiclassical analysis for diffusions and stochastic processes Vassili N. Kolokoltsov |
| title_fullStr | Semiclassical analysis for diffusions and stochastic processes Vassili N. Kolokoltsov |
| title_full_unstemmed | Semiclassical analysis for diffusions and stochastic processes Vassili N. Kolokoltsov |
| title_short | Semiclassical analysis for diffusions and stochastic processes |
| title_sort | semiclassical analysis for diffusions and stochastic processes |
| topic | Diffusionsprozess (DE-588)4274463-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Quasiklassische Näherung (DE-588)4296820-3 gnd |
| topic_facet | Diffusionsprozess Stochastischer Prozess Quasiklassische Näherung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008872691&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT kolokolcovvassilijn semiclassicalanalysisfordiffusionsandstochasticprocesses |