Stochastic tools in mathematics and science:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
|
| Edition: | 2. ed. |
| Series: | Surveys and tutorials in the applied mathematical sciences
1 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | X, 162 S. graph. Darst. |
| ISBN: | 9781441910011 |
Staff View
MARC
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| 100 | 1 | |a Chorin, Alexandre Joel |e Verfasser |0 (DE-588)109435303 |4 aut | |
| 245 | 1 | 0 | |a Stochastic tools in mathematics and science |c Alexandre J. Chorin ; Ole H. Hald |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a X, 162 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Prefaces
v
Contents
ix
Chapter
1.
Preliminaries
1
1.1.
Least Squares Approximation
1
1.2.
Orthonormal
Bases
6
1.3.
Fourier Series
9
1.4.
Fourier Transform
12
1.5.
Exercises
IG
1.6.
Bibliography
17
Chapter
2.
Probability
19
2.1.
Definitions
19
2.2.
Expected Values and Moments
22
2.3.
Monte Carlo Methods
28
2.4.
Parametric Estimation
32
2.5.
The Central Limit Theorem
34
2.6.
Conditional Probability and Conditional Expectation
37
2.7.
Bayes
Theorem
41
2.8.
Exercises
43
2.9.
Bibliography
45
Chapter
3.
Brownian Motion
47
3.1.
Definition of Brownian Motion
47
3.2.
Brownian Motion and the Heat Equation
49
3.3.
Solution of the Heat Equation by Random Walks
50
3.4.
The Wiener Measure
54
3.5.
Heat Equation with Potential 5G
3.6.
Physicists Notation for Wiener Measure G4
3.7.
Another Connection Between Brownian Motion and the
Heat Equation 6G
3.8.
First Discussion of the
Langevin
Equation G8
3.9.
Solution of a Nonlinear Differential Equation by Branching
Brownian Motion
73
x
CONTENTS
3.1Ü.
A Brief Introduction to Stochastic ODEs
75
3.11.
Exercises
77
3.12.
Bibliography
80
Chapter
4.
Stationary Stochastic Processes
83
4.1.
Weak Definition of a Stochastic Process
83
4.2.
Covariance and Spectrum
86
4.3.
Scaling and the
Inerţial
Spectrum of Turbulence
88
4.4.
Random Measures and Random Fourier Transforms
91
4.5.
Prediction for Stationary Stochastic Processes
96
4.6.
Data Assimilation
101
4.7.
Exercises
104
4.8.
Bibliography
106
Chapter
5.
Statistical Mechanics
109
5.1.
Mechanics
109
5.2.
Statistical Mechanics
112
5.3.
Entropy and Equilibrium
115
5.4.
The Ising Model
119
5.5.
Markov Chain Monte Carlo
121
5.6.
Renormalization
126
5.7.
Exercises
131
5.8.
Bibliography
134
Chapter
6.
Time-Dependent Statistical Mechanics
135
G.I. More on the
Langevin
Equation
135
6.2.
A Coupled System of Harmonic Oscillators
138
6.3.
Mathematical Addenda
140
6.4.
The Mori-Zwanzig Formalism
145
6.5.
More on Fluctuation-Dissipation Theorems
150
6.6.
Scale Separation and Weak Coupling
152
6.7.
Long Memory and the f-Model
153
6.8.
Exercises
156
6.9.
Bibliography
157
Index
161
|
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| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T22:05:06Z |
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| isbn | 9781441910011 |
| language | English |
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| series2 | Surveys and tutorials in the applied mathematical sciences |
| spelling | Chorin, Alexandre Joel Verfasser (DE-588)109435303 aut Stochastic tools in mathematics and science Alexandre J. Chorin ; Ole H. Hald 2. ed. New York, NY Springer 2009 X, 162 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Surveys and tutorials in the applied mathematical sciences 1 Stochastic processes Stochastik (DE-588)4121729-9 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Stochastik (DE-588)4121729-9 s DE-604 Angewandte Mathematik (DE-588)4142443-8 s Stochastisches Modell (DE-588)4057633-4 s Hald, Ole H. Verfasser (DE-588)139218939 aut Erscheint auch als Online-Ausgabe 978-1-4419-1002-8 Surveys and tutorials in the applied mathematical sciences 1 (DE-604)BV021500680 1 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2667970&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018668755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chorin, Alexandre Joel Hald, Ole H. Stochastic tools in mathematics and science Surveys and tutorials in the applied mathematical sciences Stochastic processes Stochastik (DE-588)4121729-9 gnd Stochastisches Modell (DE-588)4057633-4 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| subject_GND | (DE-588)4121729-9 (DE-588)4057633-4 (DE-588)4142443-8 |
| title | Stochastic tools in mathematics and science |
| title_auth | Stochastic tools in mathematics and science |
| title_exact_search | Stochastic tools in mathematics and science |
| title_full | Stochastic tools in mathematics and science Alexandre J. Chorin ; Ole H. Hald |
| title_fullStr | Stochastic tools in mathematics and science Alexandre J. Chorin ; Ole H. Hald |
| title_full_unstemmed | Stochastic tools in mathematics and science Alexandre J. Chorin ; Ole H. Hald |
| title_short | Stochastic tools in mathematics and science |
| title_sort | stochastic tools in mathematics and science |
| topic | Stochastic processes Stochastik (DE-588)4121729-9 gnd Stochastisches Modell (DE-588)4057633-4 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| topic_facet | Stochastic processes Stochastik Stochastisches Modell Angewandte Mathematik |
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