Markov processes, semigroups and generators:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
2011
|
| Series: | De Gruyter studies in mathematics
38 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 430 S. |
| ISBN: | 9783110250107 |
Staff View
MARC
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| 100 | 1 | |a Kolokolʹcov, Vassilij N. |d 1959- |e Verfasser |0 (DE-588)121728633 |4 aut | |
| 245 | 1 | 0 | |a Markov processes, semigroups and generators |c Vassili N. Kolokoltsov |
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2011 | |
| 300 | |a XVIII, 430 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematics |v 38 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-021160076 | ||
Record in the Search Index
| _version_ | 1804143859586826240 |
|---|---|
| adam_text | Contents
Preface
γιι
Notations
χί
Standard
abbreviations
xiv
I Introduction to stochastic analysis
1
1
Tools from probability and analysis
3
1.1
Essentials of measure and probability
................. 3
1.2
Characteristic functions
......................... 13
1.3
Conditioning
.............................. 16
1.4
Infinitely divisible and stable distributions
............... 21
1.5
Stable laws as the Holtzmark distributions
............... 27
1.6
Unimodality of probability laws
.................... 29
1.7
Compactness for function spaces and measures
............ 35
1.8
Fractional derivatives and pseudo-differential operators
........ 42
1.9
Propagators and semigroups
...................... 48
2
Brownian motion (BM)
58
2.1
Random processes: basic notions
.................... 58
2.2
Definition and basic properties of BM
................. 62
2.3
Construction via broken-line approximation
.............. 66
2.4
Construction via Hilbert-space methods
................ 69
2.5
Construction via Kolmogorov
s
continuity
............... 71
2.6
Construction via random walks and tightness
............ . 73
2.7
Simplest applications of martingales
.................. 76
2.8
Skorohod embedding and the
invariance
principle
........... 78
2.9
More advanced Hubert space methods: Wiener chaos and stochastic
integral
................................. 81
2.10
Fock spaces, Hermite polynomials and Malliavin calculus
....... 87
2.11
Stationarity:
OU
processes and Holtzmark fields
............ 91
3
Markov processes and martingales
94
3.1
Definition of Levy processes
...................... 94
3.2
Poisson
processes and integrals
..................... 96
3.3
Construction
of Levy
processes
..................... 103
3.4
Subordinated
.............................. 108
3.5
Markov processes, semigroups and propagators
............ 110
3.6
Feller processes and conditionally positive operators
......... 115
3.7
Diffusions and jump-type Markov processes
.............. 125
3.8
Markov processes on quotient spaces and reflections
......... 130
3.9
Martingales
...............................132
3.10
Stopping times and optional sampling
................. 138
3.11
Strong Markov property; diffusions as Feller processes with continu¬
ous paths
................................ 143
3.12
Reflection principle and passage times
................. 147
SDE, *DE and martingale problems
152
4.1
Markov semigroups and evolution equations
.............. 152
4.2
The Dirichlet problem for diffusion operators
............. 158
4.3
The stationary Feynman-Kac formula
................. 162
4.4
Diffusions with variable drift, Ornstein-Uhlenbeck processes
..... 165
4.5
Stochastic integrals and SDE based on Levy processes
........ 167
4.6
Markov property and regularity of solutions
.............. 172
4.7
Stochastic integrals and quadratic variation for square-integrable mar¬
tingales
................................. 178
4.8
Convergence of processes and semigroups
............... 187
4.9
Weak convergence of martingales
................... 193
4.10
Martingale problems and Markov processes
.............. 195
4.11
Stopping and localization
........................ 199
II Markov processes and beyond
203
5
Processes in Euclidean spaces
204
5.1
Direct analysis of regularity and well-posedness
............ 205
5.2
Introduction to sensitivity analysis
................... 213
5.3
The Lie-Trotter type limits and
Γ
-products
.............. 213
5.4
Martingale problems for Levy type generators: existence
....... 221
5.5
Martingale problems for Levy type generators: moments
....... 226
5.6
Martingale problems for Levy type generators: unbounded coefficients
228
5.7
Decomposable generators
........................ 231
5.8
SDEs driven by nonlinear Levy noise
................. 240
5.9
Stochastic
monotonicity
and duality
.................. 250
5.10
Stochastic scattering
.......................... 255
5.11
Nonlinear Markov chains, interacting particles and deterministic pro¬
cesses
.................................. 257
5.12
Comments
................................ 262
Processes in domains with a boundary
270
6.1
Stopped processes and boundary points
................ 270
6.2
Dirichlet problem and mixed initial-boundary problem
........ 274
6.3
The method of Lyapunov functions
................... 280
6.4
Local criteria for boundary points
................... 282
6.5
Decomposable generators in R^_
.................... 286
6.6
Gluing boundary
............................ 290
6.7
Processes on the half-line
........................ 292
6.8
Generators of reflected processes
.................... 293
6.9
Application to interacting particles: stochastic LLN
.......... 295
6.10
Application to evolutionary games
................... 304
6.11
Application to finances: barrier options, credit derivatives, etc
..... 307
6.12
Comments
................................ 308
Heat kernels for stable-like processes
310
7.1
One-dimensional stable laws: asymptotic expansions
......... 310
7.2
Stable laws: asymptotic expansions and identities
........... 314
7.3
Stable laws: bounds
........................... 319
7.4
Stable laws: auxiliary convolution estimates
.............. 323
7.5
Stable-like processes: heat kernel estimates
.............. 328
7.6
Stable-like processes: Feller property
................. 335
7.7
Application to sample-path properties
................. 336
7.8
Application to stochastic control
.................... 340
7.9
Application to
Langevin
equations driven by a stable noise
...... 345
7.10
Comments
................................ 348
CTRW and fractional dynamics
351
8.1
Convergence of Markov semigroups and processes
.......... 351
8.2
Diffusive approximations for random walks and CLT
......... 354
8.3
Stable-like limits for position-dependent random walks
........ 355
8.4
Subordination by hitting times and generalized fractional evolutions
. 361
8.5
Limit theorems for position dependent CTRW
............. 369
8.6
Comments
................................ 371
Complex Markov chains and Feynman integral
373
9.1
Infinitely-divisible complex distributions and complex Markov chains
373
9.2
Path integral and perturbation theory
.................. 380
9.3
Extensions
................................ 385
9.4
Regularization of the
Schrödinger
equation by complex time or mass,
or continuous observation
........................ 390
9.5 Singular
and growing potentials, magnetic fields and curvilinear state
spaces
.................................. 393
9.6
Fock-space representation
....................... 398
9.7
Comments
................................ 400
Bibliography
403
Index
425
|
| any_adam_object | 1 |
| author | Kolokolʹcov, Vassilij N. 1959- |
| author_GND | (DE-588)121728633 |
| author_facet | Kolokolʹcov, Vassilij N. 1959- |
| author_role | aut |
| author_sort | Kolokolʹcov, Vassilij N. 1959- |
| author_variant | v n k vn vnk |
| building | Verbundindex |
| bvnumber | BV037246675 |
| classification_rvk | SK 260 SK 820 |
| ctrlnum | (OCoLC)711832828 (DE-599)BVBBV037246675 |
| dewey-full | 519.233 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.233 |
| dewey-search | 519.233 |
| dewey-sort | 3519.233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV037246675 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:54:21Z |
| institution | BVB |
| isbn | 9783110250107 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021160076 |
| oclc_num | 711832828 |
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| physical | XVIII, 430 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Kolokolʹcov, Vassilij N. 1959- Verfasser (DE-588)121728633 aut Markov processes, semigroups and generators Vassili N. Kolokoltsov Berlin [u.a.] de Gruyter 2011 XVIII, 430 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 38 Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Halbgruppe (DE-588)4022990-7 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s Halbgruppe (DE-588)4022990-7 s Gruppentheorie (DE-588)4072157-7 s DE-604 Erscheint auch als Online-Ausgabe 978-3-11-025011-4 De Gruyter studies in mathematics 38 (DE-604)BV000005407 38 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021160076&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kolokolʹcov, Vassilij N. 1959- Markov processes, semigroups and generators De Gruyter studies in mathematics Gruppentheorie (DE-588)4072157-7 gnd Markov-Prozess (DE-588)4134948-9 gnd Halbgruppe (DE-588)4022990-7 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4134948-9 (DE-588)4022990-7 |
| title | Markov processes, semigroups and generators |
| title_auth | Markov processes, semigroups and generators |
| title_exact_search | Markov processes, semigroups and generators |
| title_full | Markov processes, semigroups and generators Vassili N. Kolokoltsov |
| title_fullStr | Markov processes, semigroups and generators Vassili N. Kolokoltsov |
| title_full_unstemmed | Markov processes, semigroups and generators Vassili N. Kolokoltsov |
| title_short | Markov processes, semigroups and generators |
| title_sort | markov processes semigroups and generators |
| topic | Gruppentheorie (DE-588)4072157-7 gnd Markov-Prozess (DE-588)4134948-9 gnd Halbgruppe (DE-588)4022990-7 gnd |
| topic_facet | Gruppentheorie Markov-Prozess Halbgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021160076&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT kolokolʹcovvassilijn markovprocessessemigroupsandgenerators |