Models of random processes: a handbook for mathematicians and engineers
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Boca Raton [u.a.]
CRC Press
1996
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | 446 S. |
| ISBN: | 0849328705 |
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MARC
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| 240 | 1 | 0 | |a Slučajnye processy |
| 245 | 1 | 0 | |a Models of random processes |b a handbook for mathematicians and engineers |c I. N. Kovalenko ; N. Yu. Kuznetsov ; V. M. Shurenkov |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 1996 | |
| 300 | |a 446 S. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 7 | |a Stochastische processen |2 gtt | |
| 650 | 4 | |a Stochastic processes | |
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| 700 | 1 | |a Kuznecov, Nikolaj Ju. |e Verfasser |4 aut | |
| 700 | 1 | |a Šurenkov, Valentin M. |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1809768401526063104 |
|---|---|
| adam_text |
Contents
Preface 9
Preface to the Russian Edition 9
Introduction 11
1 Definitions and General Properties of Random Processes 19
1.1 Definition of a Random Process Via a Probability Measure
over the Path Function Space 19
1.2 Definition of a Random Process Via Multidimensional Dis¬
tributions 21
1.3 Equivalence of Random Processes. Measurability. Separabi¬
lity 23
1.4 Stochastic Continuity 24
1.5 Definition of a Random Process Via Mean and Covariance
Functions 26
1.6 Mean Square Continuity 27
1.7 Random Processes with Continuous Path Functions 28
1.8 Random Processes without Discontinuities of the Second
Kind 30
1.9 Convergence of Random Processes 31
1.10 Invariance Principle 32
1.11 Ergodicity 34
1.12 References 37
2 Classification of Random Processes 39
2.1 State Space and a Parametric Set 39
2.2 Stationary in the Broad Sense Random Processes 40
2.3 Stationary Random Processes and Random Processes with
Stationary Increments 42
3
4 CONTENTS
2.4 Random Processes with Independent Increments 43
2.5 Point Processes. Memoryless Property 44
2.6 Markov Processes 46
2.7 Semi Markov Processes 48
2.8 Renewal Processes (Recurrent Point Processes) 50
2.9 Regenerative Processes 51
2.10 Gaussian Processes 53
2.11 Martingales and Semi Martingales 53
2.12 References 55
3 Discrete Time Markov Chains 57
3.1 Definitions and Elementary Relations 57
3.2 Classification of States of a Markov Chain 60
3.3 Ergodic Theorems 62
3.4 Method of Generating Functions 65
3.5 Unbounded Random Walk 67
3.6 Bounded Random Walk 69
3.7 References 73
4 Main Classes of Constructively Defined Random Processes 75
4.1 Poisson Process 75
4.2 Continuous Time Markov Chains 78
4.3 Markov Process in a Finite or Countable Phase Space . 88
4.4 Birth and Death Process 92
4.5 Application of Birth and Death Processes in Queueing Theory
and Reliability Theory 95
4.6 Main Relations for a Semi Markov Process 99
4.7 Applications of Semi Markov Processes 103
4.8 Linewise Markov Process 104
4.9 Shot Noise Process 106
4.10 References 108
5 Random Processes with Independent Increments 111
5.1 Multidimensional Brownian Motion Ill
5.2 Convergence of Sums of Infinitely Small Random Variables
to the Process of Brownian Motion 113
5.3 Characterization of a General Process with Independent In¬
crements 115
5.4 Properties of Path Functions 118
5.5 Convergence of Sums of Independent Random Variables to a
Process with Independent Increments 121
5.6 Distribution of a Functional of the Process 122
CONTENTS 5
5.7 References 124
6 Processes Associated with a Poisson Process 127
6.1 Some Properties of Point Processes. Probability Generating
Functional 127
6.2 Cluster Processes 131
6.3 Secondary Processes 135
6.4 Self Exciting and Mutually Exciting Point Processes . 137
6.5 Doubly Stochastic Poisson Process (Cox Process) 140
6.6 Bivariate Poisson Process 145
6.7 Gauss Poisson Process 147
6.8 References 150
7 Random Flows of Events 153
7.1 Main Definitions 153
7.2 Random Memoryless Flows 156
7.3 Stationary Flows 160
7.4 Flows with Bounded Aftereffect 161
7.5 Superposition of Point Processes 162
7.6 Limit Theorems for Thinned Flows , . . . 165
7.7 Marked Point Processes. Main Definitions j. 169
7.8 Palm Distribution 171
7.9 Processes with Embedded Marked Point Processes 174
7.10 Principle of Intensity Conservation 175
7.11 References 178
8 Classes of Constructively Denned Random Processes 181
8.1 Chains with Complete Connections 181
8.2 Processes Associated with Semi Markov Process 184
8.3 Some Generalizations of Regenerative Processes 189
8.4 Cumulative Processes 193
8.5 Theory of Counters 196
8.6 Cascade Processes 197
8.7 Extremal Processes 198
8.8 Piecewise Linear Markov Processes 201
8.9 References 203
9 Some Special Classes of Processes 207
9.1 Stable Processes 207
9.2 Cauchy Process 210
9.3 x2 Process, Bessel and Rayleigh Processes 211
9.4 Ornstein Uhlenbeck Process 214
6 CONTENTS
9.5 Subadditive Processes 218
9.6 Random Fields with Independent Increments 220
9.7 Periodic Random Processes 223
9.8 Random Processes Used by Description of Complex Systems 225
9.9 References 228
10 Stability of Random Processes 233
10.1 Stability of Complex Systems 233
10.2 Boundedness of Random Processes 235
10.3 Stability of Markov Chains 236
10.4 Method of Innovations 241
10.5 References 247
11 Random Processes of the Statistical Radio Engineering 249
11.1 Power Spectrum of a Stationary Random Process 249
11.2 Wide Band and Narrow Band Processes 251
11.3 Random Process with a Discrete Spectrum 253
11.4 Mutual Power Spectrum 255
11.5 Envelope and Phase of a Random Process 256
11.6 Representation of Narrow Band Processes 258
11.7 Envelope and Phase of a Gaussian Process . 259
11.8 Impulse Random Processes 260
11.9 Some Types of Impulse Processes 262
11.10 References 265
12 Renewal Theory 267
12.1 Renewal Equation 267
12.2 Renewal Process 274
12.3 Rate of the Convergence 276
12.4 Uniform Theorems 280
12.5 Transient Phenomena 282
12.6 Markov Renewal Equation 285
12.7 References 289
13 Branching Processes 291
13.1 Galton Watson Processes 291
13.2 Bellman Harris Processes 299
13.3 Markov Branching Processes . 305
13.4 Sevastyanov Model 311
13.5 Processes with Several Types of Particles 316
13.6 Jirina Processes 334
13.7 Some Other Models of Branching 341
CONTENTS 7
13.8 References 351
14 Ergodic Theory and Stationary Processes 355
14.1 Stationary Processes 355
14.2 Recurrent Markov Chains 362
14.3 Semi Markov Processes 367
14.4 Level Crossings 374
14.5 Covariance Theory 381
14.6 References 384
15 Markov Processes 387
15.1 Transition Functions 387
15.2 Infinitesimal Characteristics 393
15.3 Diffusion Processes 400
15.4 References 405
16 Statistics for Some Classes of Random Processes 407
16.1 Parameter Estimation for Flows of Homogeneous Events . 407
16.2 Regression Analysis 412
16.3 Analysis of the Trend in a Poisson Flow of Events 414
16.4 Statistics of Queueing Systems 416
16.5 Statistical Analysis of Markov and Semi Markov Processes 418
16.6 References 421
17 Simulation of Random Processes 423
17.1 Monte Carlo Method 423
17.2 Random and Pseudorandom Numbers 425
17.3 Transformations of Random Variables and Sequences . . . 427
17.4 Modelling of Markov Chains 427
17.5 Modelling of a Markov Process with a Finite Phase Space . 428
17.6 Modelling of Semi Markov Processes 428
17.7 Modelling of Regenerative Processes 429
17.8 Modelling of Brownian Motion and Some Related Processes 430
17.9 Modelling of Processes with Independent Increments . . . 431
17.10 Modelling of Gaussian Processes 432
17.11 References 433
Index 435 |
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| author | Kovalenko, Igorʹ N. 1934-2019 Kuznecov, Nikolaj Ju Šurenkov, Valentin M. |
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| id | DE-604.BV011105157 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-10T00:54:02Z |
| institution | BVB |
| isbn | 0849328705 |
| language | English Russian |
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| physical | 446 S. |
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| spelling | Kovalenko, Igorʹ N. 1934-2019 Verfasser (DE-588)104315490 aut Slučajnye processy Models of random processes a handbook for mathematicians and engineers I. N. Kovalenko ; N. Yu. Kuznetsov ; V. M. Shurenkov Boca Raton [u.a.] CRC Press 1996 446 S. txt rdacontent n rdamedia nc rdacarrier Aus dem Russ. übers. Stochastische processen gtt Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 Kuznecov, Nikolaj Ju. Verfasser aut Šurenkov, Valentin M. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007440323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kovalenko, Igorʹ N. 1934-2019 Kuznecov, Nikolaj Ju Šurenkov, Valentin M. Models of random processes a handbook for mathematicians and engineers Stochastische processen gtt Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Models of random processes a handbook for mathematicians and engineers |
| title_alt | Slučajnye processy |
| title_auth | Models of random processes a handbook for mathematicians and engineers |
| title_exact_search | Models of random processes a handbook for mathematicians and engineers |
| title_full | Models of random processes a handbook for mathematicians and engineers I. N. Kovalenko ; N. Yu. Kuznetsov ; V. M. Shurenkov |
| title_fullStr | Models of random processes a handbook for mathematicians and engineers I. N. Kovalenko ; N. Yu. Kuznetsov ; V. M. Shurenkov |
| title_full_unstemmed | Models of random processes a handbook for mathematicians and engineers I. N. Kovalenko ; N. Yu. Kuznetsov ; V. M. Shurenkov |
| title_short | Models of random processes |
| title_sort | models of random processes a handbook for mathematicians and engineers |
| title_sub | a handbook for mathematicians and engineers |
| topic | Stochastische processen gtt Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastische processen Stochastic processes Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007440323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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