Probabilistic models for nonlinear partial differential equations: lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22 - 30, 1995
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1996
|
| Schriftenreihe: | Lecture notes in mathematics
1627 Centro Internazionale Matematico Estivo: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) 1993,3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 301 S. |
| ISBN: | 3540613978 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Table of Contents
Preface V
Weak Convergence of Stochastic Integrals and Differential
Equations
Thomas G. Kurtz and Philip E. Protter 1
1. Semimartingales 1
2. Stochastic Integration 4
3. Quadratic Variation 8
4. Change of Variables 11
5. Stochastic Differential Equations 14
6. The Skorohod Topology and Weak Convergence 16
7. Weak Convergence of Stochastic Integrals 21
8. Weak Convergence of Stochastic Differential Equations 31
9. Applications to Numerical Analysis of SDE s 38
Asymptotic Behaviour of some interacting particle systems;
McKean Vlasov and Boltzmann models
Sylvie Meleard 42
1. Introduction 42
2. The physical equations, the associated nonlinear martingale prob¬
lems and some related particle systems 45
2.1 The McKean Vlasov model 45
2.2 The Boltzmann equation and some associated particle systems. 49
2.3 The Boltzmann equation with Vlasov terms and generalized
interacting systems of diffusions with jumps 54
3. Propagation of chaos and convergence rate in variation norm for the
Boltzmann model 56
3.1 Propagation of chaos in variation norm 56
3.2 Algorithms for the Boltzmann equation 63
VIII
4. Propagation of chaos for exchangeable mean field systems of diffu¬
sions with jumps 65
4.1 The propagation of chaos 65
4.2 Proof of Theorem 4.4 67
4.3 Empirical measures as probability measures on the path space
or as processes with probability measure values 70
5. Convergence of the fluctuations for the McKean Vlasov model 73
5.1 Some pathwise estimations 73
5.2 Tightness of the Fluctuation Process 78
5.3 Uniqueness and characterization of the fluctuation limit process 82
6. Appendix: Weighted Sobolev spaces 90
Kinetic limits for stochastic particle systems
Mario Pulvirenti 96
1. Introduction 96
2. Scalar Conservation Laws 101
3. Kinetic Limits 110
4. Cluster Expansion 116
5. Concluding remarks 124
A statistical physics approach to large networks
Carl Graham 127
1. Various network models and their difficulties 128
1.1 A generalized star shaped loss network 128
1.2 A fully connected loss network with alternate routing 131
1.3 A general class of networks 133
2. Asymptotic behavior of the networks 134
2.1 The chaos hypothesis and the empirical measures 134
2.2 The limit Boltzmann tree and Boltzmann processes 138
2.3 Propagation of chaos and slight symmetry 139
3. Speed of convergence and fluctuations 140
3.1 The star shaped network 140
3.2 The network with alternate routing 145
Probabilistic Numerical Methods for Partial Differential
Equations: Elements of Analysis
Denis Talay 148
1. Notation 148
2. The Euler and Milshtein schemes for SDE s 149
3. Monte Carlo methods for parabolic PDE s 152
3.1 Principle of the method 152
3.2 Introduction to the error analysis 154
3.3 Smooth functions /(¦) 158
IX
3.4 Non smooth functions /(•) 159
3.5 Extensions 165
3.6 Newton s variance reduction technique 168
3.7 Lepingle s reflected Euler scheme 169
3.8 The stationary case 171
4. Introduction to the stochastic particle methods 174
5. The Chorin Puckett method for convection reaction diffusion equa¬
tions 178
6. One dimensional Mc Kean Vlasov equations 184
7. The Burgers equation 190
Weak convergence of stochastic integrals and differential
equations II: Infinite dimensional case
Thomas G. Kurtz and Philip E. Protter 197
1. Introduction 197
2. Semimartingale random measures 199
2.1 Moment estimates for martingale random measures 203
2.2 A convergence theorem for counting measures 206
3. H^ semimartingales 210
3.1 Finite dimensional approximations 210
3.2 Integral estimates 211
3.3 .ff# semimartingale integrals 214
3.4 Predictable integrands 218
3.5 Examples 220
4. Convergence of stochastic integrals 221
5. Convergence in infinite dimensional spaces 224
5.1 Integrals with infinite dimensional range 224
5.2 Convergence theorem 227
5.3 Verification of standardness 228
5.4 Equicontinuity of stochastic integrals 232
6. Consequences of the uniform tightness condition 235
7. Stochastic differential equations 244
7.1 Uniqueness for stochastic differential equations 245
7.2 Sequences of stochastic differential equations 248
8. Markov processes 251
9. Infinite systems 255
9.1 Systems driven by Poisson random measures 255
9.2 Uniqueness for general systems 257
9.3 Convergence of sequences of systems 259
10. McKean Vlasov limits 261
11. Stochastic partial differential equations 264
11.1 Estimates for stochastic convolutions 266
11.2 Eigenvector expansions 270
11.3 Particle representations 271
X
12. Examples 273
12.1 Averaging 273
12.2 Diffusion approximations for Markov chains 275
12.3 Feller diffusion approximation for Wright Fisher model 276
12.4 Limit theorems for jump processes 277
12.5 An Euler scheme 279
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| dewey-full | 510 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 519 - Probabilities and applied mathematics |
| dewey-raw | 510 519.2 |
| dewey-search | 510 519.2 |
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| discipline | Mathematik |
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| id | DE-604.BV010804003 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:59:10Z |
| institution | BVB |
| isbn | 3540613978 |
| language | German |
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| series | Lecture notes in mathematics Centro Internazionale Matematico Estivo: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) |
| series2 | Lecture notes in mathematics Centro Internazionale Matematico Estivo: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) |
| spelling | Probabilistic models for nonlinear partial differential equations lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22 - 30, 1995 C. Graham ... Ed.: D. Talay ... Berlin [u.a.] Springer 1996 X, 301 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1627 Centro Internazionale Matematico Estivo: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) 1993,3 Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Schwache Konvergenz (DE-588)4180292-5 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1995 Montecatini Terme gnd-content Stochastisches Integral (DE-588)4126478-2 s Schwache Konvergenz (DE-588)4180292-5 s DE-604 Stochastische Differentialgleichung (DE-588)4057621-8 s Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Graham, Carl Sonstige oth Talay, Denis Sonstige (DE-588)114468907 oth Lecture notes in mathematics 1627 (DE-604)BV000676446 1627 Centro Internazionale Matematico Estivo: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) 1993,3 (DE-604)BV000903443 1995,1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007217722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Probabilistic models for nonlinear partial differential equations lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22 - 30, 1995 Lecture notes in mathematics Centro Internazionale Matematico Estivo: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Stochastisches Integral (DE-588)4126478-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Schwache Konvergenz (DE-588)4180292-5 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4126478-2 (DE-588)4128900-6 (DE-588)4180292-5 (DE-588)4079013-7 (DE-588)4057621-8 (DE-588)1071861417 |
| title | Probabilistic models for nonlinear partial differential equations lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22 - 30, 1995 |
| title_auth | Probabilistic models for nonlinear partial differential equations lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22 - 30, 1995 |
| title_exact_search | Probabilistic models for nonlinear partial differential equations lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22 - 30, 1995 |
| title_full | Probabilistic models for nonlinear partial differential equations lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22 - 30, 1995 C. Graham ... Ed.: D. Talay ... |
| title_fullStr | Probabilistic models for nonlinear partial differential equations lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22 - 30, 1995 C. Graham ... Ed.: D. Talay ... |
| title_full_unstemmed | Probabilistic models for nonlinear partial differential equations lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22 - 30, 1995 C. Graham ... Ed.: D. Talay ... |
| title_short | Probabilistic models for nonlinear partial differential equations |
| title_sort | probabilistic models for nonlinear partial differential equations lectures given at the 1st session of the centro internazionale matematico estivo c i m e held in montecatini terme italy may 22 30 1995 |
| title_sub | lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, May 22 - 30, 1995 |
| topic | Stochastisches Integral (DE-588)4126478-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Schwache Konvergenz (DE-588)4180292-5 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Stochastisches Integral Nichtlineare partielle Differentialgleichung Schwache Konvergenz Wahrscheinlichkeitstheorie Stochastische Differentialgleichung Konferenzschrift 1995 Montecatini Terme |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007217722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 (DE-604)BV000903443 |
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