Random processes for classical equations of mathematical physics:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht [u.a.]
Kluwer
1989
|
| Series: | Mathematics and its applications / Soviet series
34 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 281 S. |
| ISBN: | 079230036X |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Series Editor s Preface vii
Preface ix
Notation xix
CHAPTER 1. Markov Processes and Integral Equations 1
1.1. Breaking off Markov chains and linear integral equations 1
1.2. Markov processes with continuous time and linear evolutionary
equations 9
1.3. Convergent Markov chains and some boundary values problems 13
1.4. Markov chains and nonlinear integral equations 32
CHAPTER 2. First Boundary Value Problem for the Equation of the
Elliptic Type 41
2.1. Statement of the problem and notation 41
2.2. Green formula and the mean value theorem 42
2.3. Construction of a random process and an algorithm for the
solution of the problem 50
2.4. Methods for simulation of a Markov chain 57
2.5. Estimation of the variance of a random variable fr, 61
CHAPTER 3. Equations with Polynomial Nonlinearity 63
3.1. Preliminary examples and notation 63
3.2. Representation of solutions of integral equations with polynomial
nonlinearity 66
3.3. Definition of probability measures and the simplest estimators 71
3.4. Probabilistic solution of nonlinear equations on measures 75
CHAPTER 4. Probabilistic Solution of Some Kinetic Equations 84
4.1. Deterministic motion of particles 84
4.2. Computational aspects of the simulation of a collision
process 91
4.3. Random trajectories of particles. The construction of the basic
process 92
4.4. Collision processes 97
4.5. Auxiliary results 100
4.6. Lemmas on certain integral equations 103
4.7. Uniqueness of the solution of the (X, T, H) equation 106
4.8. Probabilistic solution of the interior boundary value problem
for the regularized Boltzmann equation 109
4.9. Estimation of the computational labour requirements 115
vi CONTENTS
CHAPTER 5. Various Boundary Value Problems Related to the Laplace
Operator 118
5.1. Parabolic means and a solution of the mixed problem for the
heat equation 118
5.2. Exterior Dirichlet problem for the Laplace equation 122
5.3. Solution of the Neumann problem 127
5.4. Branching random walks on spheres and the Dirichlet problem
for the equation Au = u2 135
5.5. Special method for the solution of the Dirichlet problem
for the Helmholtz equation 145
5.6. Probabilistic solution of the wave equation in the case of an
infinitely differentiable solution 147
5.7. Another approach to the solution of hyperbolic equations 162
5.8. Probabilistic representation of the solution of boundary value
problems for an inhomogeneous telegraph equation 169
5.9. Cauchy problem for the Schrodinger equation 173
CHAPTER 6. Generalized Principal Value Integrals and Related
Random Processes 177
6.1. Random processes related to linear equations 178
6.2. Nonlinear equations 190
6.3. On the representation of a solution of nonlinear equations as a
generalized principal value integral 195
6.4. Principal part of the operator and the Monte Carlo method 202
CHAPTER 7. Interacting Diffusion Processes and Nonlinear Parabolic
Equations 213
7.1. Propagation of chaos and the law of large numbers 213
7.2. Interacting Markov processes and nonlinear equations. Heuristic
considerations 217
7.3. Weakly interacting diffusions 226
7.4. Moderately interacting diffusions 238
7.5. On one method of numerical solution of systems of stochastic
differential equations 259
Bibliographical Notes 268
References 270
Additional References 273
Index 278
|
| any_adam_object | 1 |
| author | Ermakov, Sergej M. 1930- Nekrutkin, Vladimir V. Sipin, Alexander |
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| author_facet | Ermakov, Sergej M. 1930- Nekrutkin, Vladimir V. Sipin, Alexander |
| author_role | aut aut aut |
| author_sort | Ermakov, Sergej M. 1930- |
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| classification_tum | MAT 606f |
| ctrlnum | (OCoLC)18587847 (DE-599)BVBBV003571440 |
| dewey-full | 530.1/592 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/592 |
| dewey-search | 530.1/592 |
| dewey-sort | 3530.1 3592 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T16:02:05Z |
| institution | BVB |
| isbn | 079230036X |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002273539 |
| oclc_num | 18587847 |
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| physical | XX, 281 S. |
| publishDate | 1989 |
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| publisher | Kluwer |
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| series2 | Mathematics and its applications / Soviet series |
| spelling | Ermakov, Sergej M. 1930- Verfasser (DE-588)120951479 aut Slučajnye processy dlja rešenija klassičeskich uravnenij matematičeskoj fiziki Random processes for classical equations of mathematical physics by S. M. Ermakov, V. V. Nekrutin and A. S. Sipin Dordrecht [u.a.] Kluwer 1989 XX, 281 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 34 Mathematische Physik Mathematical physics Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Nekrutkin, Vladimir V. Verfasser (DE-588)12870215X aut Sipin, Alexander Verfasser (DE-588)1203629060 aut Soviet series Mathematics and its applications 34 (DE-604)BV004708148 34 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002273539&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ermakov, Sergej M. 1930- Nekrutkin, Vladimir V. Sipin, Alexander Random processes for classical equations of mathematical physics Mathematische Physik Mathematical physics Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4037952-8 |
| title | Random processes for classical equations of mathematical physics |
| title_alt | Slučajnye processy dlja rešenija klassičeskich uravnenij matematičeskoj fiziki |
| title_auth | Random processes for classical equations of mathematical physics |
| title_exact_search | Random processes for classical equations of mathematical physics |
| title_full | Random processes for classical equations of mathematical physics by S. M. Ermakov, V. V. Nekrutin and A. S. Sipin |
| title_fullStr | Random processes for classical equations of mathematical physics by S. M. Ermakov, V. V. Nekrutin and A. S. Sipin |
| title_full_unstemmed | Random processes for classical equations of mathematical physics by S. M. Ermakov, V. V. Nekrutin and A. S. Sipin |
| title_short | Random processes for classical equations of mathematical physics |
| title_sort | random processes for classical equations of mathematical physics |
| topic | Mathematische Physik Mathematical physics Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische Physik Mathematical physics Stochastic processes Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002273539&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
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