Random perturbation methods with applications in science and engineering:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
2002
|
| Series: | Applied mathematical sciences
150 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 488 S. Illustrationen |
| ISBN: | 0387954279 |
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| adam_text | ANATOLI V. SKOROKHOD FRANK C. HOPPENSTEADT HABIB SALEHI RANDOM
PERTURBATION METHODS WITH APPLICATIONS IN SCIENCE AND ENGINEERING WITH
31 FIGURES SPRINGER CONTENTS PREFACE V INTRODUCTION 1 WHAT ARE DYNAMICAL
SYSTEMS? 1 WHAT IS RANDOM NOISE? 3 WHAT ARE ERGODIC THEOREMS? 8 WHAT
HAPPENS FOR T LARGE? 18 WHAT IS IN THIS BOOK? 21 1 ERGODIC THEOREMS 49
1.1 BIRKHOFF S CLASSICAL ERGODIC THEOREM 49 1.1.1 MIXING CONDITIONS 53
1.1.2 DISCRETE-TIME STATIONARY PROCESSES 54 1.2 DISCRETE-TIME MARKOV
PROCESSES 56 1.3 CONTINUOUS-TIME STATIONARY PROCESSES 60 1.4
CONTINUOUS-TIME MARKOV PROCESSES 61 2 CONVERGENCE PROPERTIES OF
STOCHASTIC PROCESSES 64 2.1 WEAK CONVERGENCE OF STOCHASTIC PROCESSES 64
2.1.1 WEAK COMPACTNESS IN C 66 2.2 CONVERGENCE TO A DIFFUSION PROCESS 68
2.2.1 DIFFUSION PROCESSES 68 2.2.2 WEAK CONVERGENCE TO A DIFFUSION
PROCESS 70 2.3 CENTRAL LIMIT THEOREMS FOR STOCHASTIC PROCESSES . . . .
73 VIII CONTENTS 2.3.1 CONTINUOUS-TIME MARKOV PROCESSES 73 2.3.2
DISCRETE-TIME MARKOV PROCESSES 75 2.3.3 DISCRETE-TIME STATIONARY
PROCESSES 76 2.3.4 CONTINUOUS-TIME STATIONARY PROCESSES 79 2.4 LARGE
DEVIATION THEOREMS . 80 2.4.1 CONTINUOUS-TIME MARKOV PROCESSES 81 2.4.2
DISCRETE-TIME MARKOV PROCESSES 86 3 AVERAGING 88 3.1 VOLTERRA INTEGRAL
EQUATIONS 88 3.1.1 LINEAR VOLTERRA INTEGRAL EQUATIONS 92 3.1.2 SOME
NONLINEAR EQUATIONS 97 3.2 DIFFERENTIAL EQUATIONS 99 3.2.1 LINEAR
DIFFERENTIAL EQUATIONS 101 3.3 DIFFERENCE EQUATIONS 102 3.3.1 LINEAR
DIFFERENCE EQUATIONS 105 3.4 LARGE DEVIATION FOR DIFFERENTIAL EQUATIONS
105 3.4.1 SOME AUXILIARY RESULTS 106 3.4.2 MAIN THEOREM 110 3.4.3
SYSTEMS WITH ADDITIVE PERTURBATIONS 112 4 NORMAL DEVIATIONS 114 4.1
VOLTERRA INTEGRAL EQUATIONS 114 4.2 DIFFERENTIAL EQUATIONS 120 4.2.1
MARKOV PERTURBATIONS 127 4.3 DIFFERENCE EQUATIONS 128 5 DIFFUSION
APPROXIMATION 133 5.1 DIFFERENTIAL EQUATIONS 133 5.1.1 MARKOV JUMP
PERTURBATIONS 134 5.1.2 SOME GENERALIZATIONS 140 5.1.3 GENERAL MARKOV
PERTURBATIONS 145 5.1.4 STATIONARY PERTURBATIONS 146 5.1.5 DIFFUSION
APPROXIMATIONS TO FIRST INTEGRALS ... 150 5.2 DIFFERENCE EQUATIONS 156
5.2.1 MARKOV PERTURBATIONS 156 5.2.2 DIFFUSION APPROXIMATIONS TO FIRST
INTEGRALS ... 161 5.2.3 STATIONARY PERTURBATIONS 166 6 STABILITY 172 6.1
STABILITY OF PERTURBED DIFFERENTIAL EQUATIONS 172 6.1.1 JUMP
PERTURBATIONS OF NONLINEAR EQUATIONS . . . 173 6.1.2 STATIONARY
PERTURBATIONS 182 6.2 STOCHASTIC RESONANCE FOR GRADIENT SYSTEMS 193
6.2.1 LARGE DEVIATIONS NEAR A STABLE STATIC STATE . . . 193 CONTENTS IX
6.2.2 TRANSITIONS BETWEEN STABLE STATIC STATES 198 6.2.3 STOCHASTIC
RESONANCE 199 6.3 RANDOMLY PERTURBED DIFFERENCE EQUATIONS 200 6.3.1
MARKOV PERTURBATIONS: LINEAR EQUATIONS 201 6.3.2 STATIONARY
PERTURBATIONS 203 6.3.3 MARKOV PERTURBATIONS: NONLINEAR EQUATIONS . . .
205 6.3.4 STATIONARY PERTURBATIONS 210 6.3.5 SMALL PERTURBATIONS OF A
STABLE SYSTEM 211 6.4 CONVOLUTION INTEGRAL EQUATIONS 216 6.4.1 LAPLACE
TRANSFORMS AND THEIR INVERSES 218 6.4.2 LAPLACE TRANSFORMS OF NOISY
KERNELS 222 MARKOV CHAINS WITH RANDOM TRANSITION PROBABILITIES 232 7.1
STATIONARY RANDOM ENVIRONMENT 233 7.2 WEAKLY RANDOM ENVIRONMENTS 243 7.3
MARKOV PROCESSES WITH RANDOMLY PERTURBED TRANSITION PROBABILITIES 249
7.3.1 STATIONARY RANDOM ENVIRONMENTS 249 7.3.2 ERGODIC THEOREM FOR
MARKOV PROCESSES IN RANDOM ENVIRONMENTS 253 7.3.3 MARKOV PROCESS IN A
WEAKLY RANDOM ENVIRONMENT 254 RANDOMLY PERTURBED MECHANICAL SYSTEMS 257
8.1 CONSERVATIVE SYSTEMS WITH TWO DEGREES OF FREEDOM . . . 257 8.1.1
CONSERVATIVE SYSTEMS 258 8.1.2 RANDOMLY PERTURBED CONSERVATIVE SYSTEMS .
. . 262 8.1.3 BEHAVIOR OF THE PERTURBED SYSTEM NEAR A KNOT 273 8.1.4
DIFFUSION PROCESSES ON GRAPHS 285 8.1.5 SIMULATION OF A TWO-WELL
POTENTIAL PROBLEM ... 290 8.2 LINEAR OSCILLATING CONSERVATIVE SYSTEMS
290 8.2.1 FREE LINEAR OSCILLATING CONSERVATIVE SYSTEMS . . 290 8.2.2
RANDOMLY PERTURBED LINEAR OSCILLATING SYSTEMS 293 8.3 A RIGID BODY WITH
A FIXED POINT 297 8.3.1 MOTION OF A RIGID BODY AROUND A FIXED POINT 298
8.3.2 ANALYSIS OF RANDOMLY PERTURBED MOTIONS . . . . 299 DYNAMICAL
SYSTEMS ON A TORUS 303 9.1 THEORY OF ROTATION NUMBERS 303 9.1.1
EXISTENCE OF THE ROTATION NUMBER 305 9.1.2 PURELY PERIODIC SYSTEMS 307
9.1.3 ERGODIC SYSTEMS 308 X CONTENTS 9.1.4 SIMULATION OF ROTATION
NUMBERS 310 9.2 RANDOMLY PERTURBED TORUS FLOWS 311 9.2.1 ROTATION NUMBER
IN THE PRESENCE OF NOISE . . . . 313 9.2.2 SIMULATION OF ROTATION
NUMBERS WITH NOISE . . . 321 9.2.3 RANDOMLY PERTURBED PURELY PERIODIC
SYSTEMS . . 321 9.2.4 ERGODIC SYSTEMS 329 9.2.5 PERIODIC SYSTEMS 335 10
PHASE-LOCKED LOOPS 343 10.1 THE FREE SYSTEM 346 10.1.1 THE NONRANDOM
FREE SYSTEM 347 10.1.2 EXAMPLE: SIMULATION OF THE FREE PLL SYSTEM . .
352 10.1.3 RANDOM PERTURBATIONS OF THE FREE SYSTEM . . . . 353 10.1.4
BEHAVIOR OF THE PERTURBED SYSTEM NEAR THE RUNNING PERIODIC SOLUTION 355
10.1.5 BEHAVIOR OF THE PERTURBED SYSTEM NEAR THE STABLE STATIC STATE 357
10.1.6 ERGODIC PROPERTIES OF THE PERTURBED SYSTEM . . . 360 10.2 THE
FORCED PROBLEM 362 10.2.1 SYSTEMS WITHOUT A LOOP FILTER (NONRANDOM). . .
363 10.2.2 RANDOMLY PERTURBED SYSTEMS WITHOUT A LOOP FILTER 367 10.2.3
FORCED SYSTEMS WITH NOISY INPUT SIGNALS 371 10.2.4 SIMULATION OF A
PHASE-LOCKED LOOP WITH NOISY INPUT 374 11 MODELS IN POPULATION BIOLOGY
376 11.1 MATHEMATICAL ECOLOGY 376 11.1.1 LOTKA-VOLTERA MODEL 377 11.1.2
RANDOM PERTURBATIONS OF THE LOTKA-VOLTERRA MODEL 379 11.1.3 SIMULATION
OF THE LOTKA-VOLTERRA MODEL 387 11.1.4 TWO SPECIES COMPETING FOR A
LIMITED RESOURCE 388 11.1.5 A FOOD CHAIN WITH THREE SPECIES 394 11.1.6
SIMULATION OF A FOOD CHAIN 398 11.2 EPIDEMICS 398 11.2.1 THE
KERMACK-MCKENDRICK MODEL 399 11.2.2 RANDOMLY PERTURBED EPIDEMIC MODELS
403 11.2.3 RECURRENT EPIDEMICS 407 11.2A DIFFUSION APPROXIMATION 411
11.3 DEMOGRAPHICS . . 413 11.3.1 NONLINEAR RENEWAL EQUATIONS 413 11.3.2
LINEAR RENEWAL EQUATIONS 419 11.3.3 DISCRETE-TIME RENEWAL THEORY 421
CONTENTS XI 12 GENETICS 424 12.1 POPULATION GENETICS: THE GENE POOL 425
12.1.1 THE FHW MODEL WITH STATIONARY SLOW SELECTION 426 12.1.2 RANDOM
PERTURBATION OF THE STATIONARY SLOW SELECTION MODEL 427 12.2 BACTERIAL
GENETICS: PLASMID STABILITY 431 12.2.1 PLASMID DYNAMICS 433 12.2.2
RANDOMLY PERTURBED PLASMID DYNAMICS 435 12.3 EVOLUTIONARY GENETICS: THE
GENOME 439 12.3.1 BRANCHING MARKOV PROCESS MODEL 440 12.3.2 EVOLUTION OF
THE GENOME IN A RANDOM ENVIRONMENT 447 12.3.3 EVOLUTION IN A RANDOM
ENVIRONMENT 450 A SOME NOTIONS OF PROBABILITY THEORY 452 B COMMENTARY
469 REFERENCES 472 INDEX 485
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:02:01Z |
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| isbn | 0387954279 |
| language | English |
| lccn | 2001059799 |
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| physical | XI, 488 S. Illustrationen |
| publishDate | 2002 |
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| publisher | Springer |
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| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Skorochod, Anatolij V. 1930-2011 Verfasser (DE-588)128936037 aut Random perturbation methods with applications in science and engineering Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi New York Springer 2002 XI, 488 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 150 Störungstheorie (DE-588)4128420-3 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Störungstheorie (DE-588)4128420-3 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Hoppensteadt, Frank C. 1938- Verfasser (DE-588)11268792X aut Salehi, Habib Verfasser aut Applied mathematical sciences 150 (DE-604)BV000005274 150 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009839068&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Skorochod, Anatolij V. 1930-2011 Hoppensteadt, Frank C. 1938- Salehi, Habib Random perturbation methods with applications in science and engineering Applied mathematical sciences Störungstheorie (DE-588)4128420-3 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4057630-9 (DE-588)4013396-5 |
| title | Random perturbation methods with applications in science and engineering |
| title_auth | Random perturbation methods with applications in science and engineering |
| title_exact_search | Random perturbation methods with applications in science and engineering |
| title_full | Random perturbation methods with applications in science and engineering Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi |
| title_fullStr | Random perturbation methods with applications in science and engineering Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi |
| title_full_unstemmed | Random perturbation methods with applications in science and engineering Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi |
| title_short | Random perturbation methods with applications in science and engineering |
| title_sort | random perturbation methods with applications in science and engineering |
| topic | Störungstheorie (DE-588)4128420-3 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Störungstheorie Stochastischer Prozess Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009839068&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
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