Random processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1974
|
| Edition: | 2. ed. |
| Series: | Graduate texts in mathematics
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 228 S. |
| ISBN: | 0387900853 3540900853 |
Staff View
MARC
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Record in the Search Index
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CONTENTS
Notation 2
I. Introduction 3
II. Basic Notions for Finite and Denumerable State Models 6
a. Events and Probabilities of Events 6
b. Conditional Probability, Independence, and Random Variables 10
c. The Binomial and Poisson Distributions 13
d. Expectation and Variance of Random Variables (Moments) 15
e. The Weak Law of Large Numbers and the Central Limit
Theorem 20
f. Entropy of an Experiment 29
g. Problems 32
III. Markov Chains 36
a. The Markov Assumption 36
b. Matrices with Non negative Elements (Approach of Perron
Frobenius) 44
c. Limit Properties for Markov Chains 52
d. Functions of a Markov Chain 59
e. Problems 64
IV. Probability Spaces with an Infinite Number of Sample Points 68
a. Discussion of Basic Concepts 68
b. Distribution Functions and Their Transforms 80
c. Derivatives of Measures and Conditional Probabilities 86
d. Random Processes 91
e. Problems 96
V. Stationary Processes 100
a. Definition 100
b. The Ergodic Theorem and Stationary Processes 103
c. Convergence of Conditional Probabilities 112
d. MacMillan's Theorem 114
c. Problems 118
ix
x Contents
VI. Markov Processes 120
a. Definition 120
b. Jump Processes with Continuous Time 124
c. Diffusion Processes 133
d. A Refined Model of Brownian Motion 137
e. Pathological Jump Processes 141
f. Problems 146
VII. Weakly Stationary Processes and Random Harmonic Analysis 149
a. Definition 149
b. Harmonic Representation of a Stationary Process and Random
Integrals 153
c. The Linear Prediction Problem and Autoregressive Schemes 160
d. Spectral Estimates for Normal Processes 169
e. Problems 178
VIII. Martingales 182
a. Definition and Illustrations 182
b. Optional Sampling and a Martingale Convergence Theorem 185
c. A Central Limit Theorem for Martingale Differences 191
d. Problems 197
IX. Additional Topics 200
a. A Zero One Law 200
b. Markov Chains and Independent Random Variables 201
c. A Representation for a Class of Random Processes 203
d. A Uniform Mixing Condition and Narrow Band Pass Filtering 213
e. Problems 219
References 221
Index 227 |
| any_adam_object | 1 |
| author | Rosenblatt, Murray 1926-2019 |
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| ctrlnum | (OCoLC)940737 (DE-599)BVBBV002656970 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| institution | BVB |
| isbn | 0387900853 3540900853 |
| language | English |
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| physical | X, 228 S. |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Rosenblatt, Murray 1926-2019 Verfasser (DE-588)1072191784 aut Random processes M. Rosenblatt 2. ed. New York [u.a.] Springer 1974 X, 228 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 17 Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 Graduate texts in mathematics 17 (DE-604)BV000000067 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001703566&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosenblatt, Murray 1926-2019 Random processes Graduate texts in mathematics Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Random processes |
| title_auth | Random processes |
| title_exact_search | Random processes |
| title_full | Random processes M. Rosenblatt |
| title_fullStr | Random processes M. Rosenblatt |
| title_full_unstemmed | Random processes M. Rosenblatt |
| title_short | Random processes |
| title_sort | random processes |
| topic | Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Processus stochastiques Stochastic processes Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001703566&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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