Random dynamical systems: theory and applications
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Mass.[u.a.]
Cambridge Univ. Press
2007
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Beschreibung für Leser Inhaltsverzeichnis |
| Physical Description: | XV, 463 S. |
| ISBN: | 9780521825658 0521825652 9780521532723 0521532728 |
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| adam_text | CONTENTS PREFACE PAGE IX ACKNOWLEDGMENT XIII NOTATION XV 1 DYNAMICAL
SYSTEMS 1 1.1 INTRODUCTION 1 1.2 BASIC DEFINITIONS: FIXED AND PERIODIC
POINTS 3 1.3 COMPLEXITY 11 1.3.1 LI-YORKE CHAOS AND SARKOVSKII THEOREM
11 1.3.2 A REMARK ON ROBUSTNESS OF LI-YORKE COMPLEXITY 14 1.3.3
COMPLEXITY: ALTERNATIVE APPROACHES 16 1.4 LINEAR DIFFERENCE EQUATIONS 17
1.5 INCREASING LAWS OF MOTION 20 1.6 THRESHOLDS AND CRITICAL STOCKS 26
1.7 THE QUADRATIC FAMILY 32 1.7.1 STABLE PERIODIC ORBITS 33 1.8
COMPARATIVE STATICS AND DYNAMICS 38 1.8.1 BIFURCATION THEORY 39 1.9 SOME
APPLICATIONS 46 1.9.1 THE HARROD-DOMAR MODEL 46 1.9.2 THE SOLOW MODEL 47
1.9.3 BALANCED GROWTH AND MULTIPLICATIVE PROCESSES 53 1.9.4 MODELS OF
INTERTEMPORAL OPTIMIZATION WITH A SINGLE DECISION MAKER 59 1.9.5
OPTIMIZATION WITH WEALTH EFFECTS: PERIODICITY AND CHAOS 77 1.9.6 DYNAMIC
PROGRAMMING 83 1.9.7 DYNAMIC GAMES 95 1.9.8 INTERTEMPORAL EQUILIBRIUM 98
1.9.9 CHAOS IN COBB-DOUGLAS ECONOMIES 101 V VI CONTENTS 1.10 COMPLEMENTS
AND DETAILS 104 1.11 SUPPLEMENTARY EXERCISES 113 MARKOV PROCESSES 119
2.1 INTRODUCTION 119 2.2 CONSTRUCTION OF STOCHASTIC PROCESSES 122 2.3
MARKOV PROCESSES WITH A COUNTABLE NUMBER OF STATES 126 2.4 ESSENTIAL,
INESSENTIAL, AND PERIODIC STATES OF A MARKOV CHAIN 131 2.5 CONVERGENCE
TO STEADY STATES FOR MARKOV PROCESSES ON FINITE STATE SPACES 133 2.6
STOPPING TIMES AND THE STRONG MARKOV PROPERTY OF MARKOV CHAINS 143 2.7
TRANSIENT AND RECURRENT CHAINS 150 2.8 POSITIVE RECURRENCE AND STEADY
STATE DISTRIBUTIONS OF MARKOV CHAINS 159 2.9 MARKOV PROCESSES ON
MEASURABLE STATE SPACES: EXISTENCE OF AND CONVERGENCE TO UNIQUE STEADY
STATES 176 2.10 STRONG LAW OF LARGE NUMBERS AND CENTRAL LIMIT THEOREM
185 2.11 MARKOV PROCESSES ON METRIC SPACES: EXISTENCE OF STEADY STATES
191 2.12 ASYMPTOTIC STATIONARITY 196 2.13 COMPLEMENTS AND DETAILS 201 2,
13.1 IRREDUCIBILITY AND HARRIS RECURRENT MARKOV PROCESSES 210 2.14
SUPPLEMENTARY EXERCISES 239 RANDOM DYNAMICAL SYSTEMS 245 3.1
INTRODUCTION 245 3.2 RANDOM DYNAMICAL SYSTEMS 246 3.3 EVOLUTION 247 3.4
THE ROLE OF UNCERTAINTY: TWO EXAMPLES 248 3.5 SPLITTING 250 3.5.1
SPLITTING AND MONOTONE MAPS 250 3.5.2 SPLITTING: A GENERALIZATION 255
3.5.3 THE DOEBLIN MINORIZATION THEOREM ONCE AGAIN 260 3.6 APPLICATIONS
262 3.6.1 FIRST-ORDER NONLINEAR AUTOREGRESSIVE PROCESSES (NLAR(L)) 262
CONTENTS VII 3.6.2 STABILITY OF INVARIANT DISTRIBUTIONS IN MODELS OF
ECONOMIC GROWTH 263 3.6.3 INTERACTION OF GROWTH AND CYCLES 267 3.6.4
COMPARATIVE DYNAMICS 273 3.7 CONTRACTIONS 275 3.7.1 ITERATION OF RANDOM
LIPSCHITZ MAPS 275 3.7.2 A VARIANT DUE TO DUBINS AND FREEDMAN 281 3.8
COMPLEMENTS AND DETAILS 284 3.9 SUPPLEMENTARY EXERCISES 294 4 RANDOM
DYNAMICAL SYSTEMS: SPECIAL STRUCTURES 296 4.1 INTRODUCTION 296 4.2
ITERATES OF REAL-VALUED AFFINE MAPS (AR(1) MODELS) 297 4.3 LINEAR
AUTOREGRESSIVE (LAR(/C)) AND OTHER LINEAR TIME SERIES MODELS 304 4.4
ITERATES OF QUADRATIC MAPS 310 4.5 NLAR (/C) AND NLARCH (K) MODELS 317
4.6 RANDOM CONTINUED FRACTIONS 323 4.6.1 CONTINUED FRACTIONS: EUCLID S
ALGORITHM AND THE DYNAMICAL SYSTEM OF GAUSS 324 4.6.2 GENERAL CONTINUED
FRACTIONS AND RANDOM CONTINUED FRACTIONS 325 4.6.3 BERNOULLI INNOVATION
330 4.7 NONNEGATIVITY CONSTRAINTS 336 4.8 A MODEL WITH MULTIPLICATIVE
SHOCKS, AND THE SURVIVAL PROBABILITY OF AN ECONOMIC AGENT 338 4.9
COMPLEMENTS AND DETAILS 342 5 INVARIANT DISTRIBUTIONS: ESTIMATION AND
COMPUTATION 349 5.1 INTRODUCTION 349 5.2 ESTIMATING THE INVARIANT
DISTRIBUTION 350 5.3 A SUFFICIENT CONDITION FOR V^-CONSISTENCY 351 5.3.1
YTZ-CONSISTENCY 352 5.4 CENTRAL LIMIT THEOREMS 360 5.5 THE NATURE OF THE
INVARIANT DISTRIBUTION 365 5.5.1 RANDOM ITERATIONS OF TWO QUADRATIC MAPS
367 5.6 COMPLEMENTS AND DETAILS 369 5.7 SUPPLEMENTARY EXERCISES 375 6
DISCOUNTED DYNAMIC PROGRAMMING UNDER UNCERTAINTY 379 6.1 INTRODUCTION
379 6.2 THE MODEL 380 6.2.1 OPTIMALITY AND THE FUNCTIONAL EQUATION OF
DYNAMIC PROGRAMMING 381 VIII CONTENTS 6.3 THE MAXIMUM THEOREM: A
DIGRESSION 6.3.1 CONTINUOUS CORRESPONDENCES 63.2 THE MAXIMUM THEOREM AND
THE EXISTENCE OF A MEASURABLE SELECTION 6.4 DYNAMIC PROGRAMMING WITH A
COMPACT ACTION SPACE 6.5 APPLICATIONS 6.5.1 THE AGGREGATIVE MODEL OF
OPTIMAL GROWTH UNDER UNCERTAINTY: THE DISCOUNTED CASE 6.5.2 INTERIOR
OPTIMAL PROCESSES 6.5.3 THE RANDOM DYNAMICAL SYSTEM OF OPTIMAL INPUTS
6.5.4 AC CUMUL ATION OF RI SKY C AP ITAL 6.6 COMPLEMENTS AND DETAILS
6.6.1 UPPER SEMICONTINUOUS MODEL 6.6.2 THE CONTROLLED SEMI-MARKOV MODEL
6.6.3 STATE-DEPENDENT ACTIONS ^ APPENDIX AL. METRIC SPACES:
SEPARABILITY, COMPLETENESS, AND COMPACTNESS A 1.1. SEPARABILITY AL,2,
COMPLETENESS A1.3. COMPACTNESS A2. INFINITE PRODUCTS OF METRIC SPACES
AND THE DIAGONALIZATION ARGUMENT A3. MEASURABILITY A3.1. SUBSPACES A3.2.
PRODUCT SPACES; SEPARABILITY ONCE AGAIN A3.3. THE SUPPORT OF A MEASURE
A3,4. CHANGE OF VARIABLE A4. BOREL-CANTELLI LEMMA A5. CONVERGENCE
BIBLIOGRAPHY AUTHOR INDEX SUBJECT INDEX 385 385 386 388 390 390 397 402
407 409 409 410 415 419 419 420 420 422 423 425 426 426 428 428 430 431
435 453 457
|
| adam_txt |
CONTENTS PREFACE PAGE IX ACKNOWLEDGMENT XIII NOTATION XV 1 DYNAMICAL
SYSTEMS 1 1.1 INTRODUCTION 1 1.2 BASIC DEFINITIONS: FIXED AND PERIODIC
POINTS 3 1.3 COMPLEXITY 11 1.3.1 LI-YORKE CHAOS AND SARKOVSKII THEOREM
11 1.3.2 A REMARK ON ROBUSTNESS OF LI-YORKE COMPLEXITY 14 1.3.3
COMPLEXITY: ALTERNATIVE APPROACHES 16 1.4 LINEAR DIFFERENCE EQUATIONS 17
1.5 INCREASING LAWS OF MOTION 20 1.6 THRESHOLDS AND CRITICAL STOCKS 26
1.7 THE QUADRATIC FAMILY 32 1.7.1 STABLE PERIODIC ORBITS 33 1.8
COMPARATIVE STATICS AND DYNAMICS 38 1.8.1 BIFURCATION THEORY 39 1.9 SOME
APPLICATIONS 46 1.9.1 THE HARROD-DOMAR MODEL 46 1.9.2 THE SOLOW MODEL 47
1.9.3 BALANCED GROWTH AND MULTIPLICATIVE PROCESSES 53 1.9.4 MODELS OF
INTERTEMPORAL OPTIMIZATION WITH A SINGLE DECISION MAKER 59 1.9.5
OPTIMIZATION WITH WEALTH EFFECTS: PERIODICITY AND CHAOS 77 1.9.6 DYNAMIC
PROGRAMMING 83 1.9.7 DYNAMIC GAMES 95 1.9.8 INTERTEMPORAL EQUILIBRIUM 98
1.9.9 CHAOS IN COBB-DOUGLAS ECONOMIES 101 V VI CONTENTS 1.10 COMPLEMENTS
AND DETAILS 104 1.11 SUPPLEMENTARY EXERCISES 113 MARKOV PROCESSES 119
2.1 INTRODUCTION 119 2.2 CONSTRUCTION OF STOCHASTIC PROCESSES 122 2.3
MARKOV PROCESSES WITH A COUNTABLE NUMBER OF STATES 126 2.4 ESSENTIAL,
INESSENTIAL, AND PERIODIC STATES OF A MARKOV CHAIN 131 2.5 CONVERGENCE
TO STEADY STATES FOR MARKOV PROCESSES ON FINITE STATE SPACES 133 2.6
STOPPING TIMES AND THE STRONG MARKOV PROPERTY OF MARKOV CHAINS 143 2.7
TRANSIENT AND RECURRENT CHAINS 150 2.8 POSITIVE RECURRENCE AND STEADY
STATE DISTRIBUTIONS OF MARKOV CHAINS 159 2.9 MARKOV PROCESSES ON
MEASURABLE STATE SPACES: EXISTENCE OF AND CONVERGENCE TO UNIQUE STEADY
STATES 176 2.10 STRONG LAW OF LARGE NUMBERS AND CENTRAL LIMIT THEOREM
185 2.11 MARKOV PROCESSES ON METRIC SPACES: EXISTENCE OF STEADY STATES
191 2.12 ASYMPTOTIC STATIONARITY 196 2.13 COMPLEMENTS AND DETAILS 201 2,
13.1 IRREDUCIBILITY AND HARRIS RECURRENT MARKOV PROCESSES 210 2.14
SUPPLEMENTARY EXERCISES 239 RANDOM DYNAMICAL SYSTEMS 245 3.1
INTRODUCTION 245 3.2 RANDOM DYNAMICAL SYSTEMS 246 3.3 EVOLUTION 247 3.4
THE ROLE OF UNCERTAINTY: TWO EXAMPLES 248 3.5 SPLITTING 250 3.5.1
SPLITTING AND MONOTONE MAPS 250 3.5.2 SPLITTING: A GENERALIZATION 255
3.5.3 THE DOEBLIN MINORIZATION THEOREM ONCE AGAIN 260 3.6 APPLICATIONS
262 3.6.1 FIRST-ORDER NONLINEAR AUTOREGRESSIVE PROCESSES (NLAR(L)) 262
CONTENTS VII 3.6.2 STABILITY OF INVARIANT DISTRIBUTIONS IN MODELS OF
ECONOMIC GROWTH 263 3.6.3 INTERACTION OF GROWTH AND CYCLES 267 3.6.4
COMPARATIVE DYNAMICS 273 3.7 CONTRACTIONS 275 3.7.1 ITERATION OF RANDOM
LIPSCHITZ MAPS 275 3.7.2 A VARIANT DUE TO DUBINS AND FREEDMAN 281 3.8
COMPLEMENTS AND DETAILS 284 3.9 SUPPLEMENTARY EXERCISES 294 4 RANDOM
DYNAMICAL SYSTEMS: SPECIAL STRUCTURES 296 4.1 INTRODUCTION 296 4.2
ITERATES OF REAL-VALUED AFFINE MAPS (AR(1) MODELS) 297 4.3 LINEAR
AUTOREGRESSIVE (LAR(/C)) AND OTHER LINEAR TIME SERIES MODELS 304 4.4
ITERATES OF QUADRATIC MAPS 310 4.5 NLAR (/C) AND NLARCH (K) MODELS 317
4.6 RANDOM CONTINUED FRACTIONS 323 4.6.1 CONTINUED FRACTIONS: EUCLID'S
ALGORITHM AND THE DYNAMICAL SYSTEM OF GAUSS 324 4.6.2 GENERAL CONTINUED
FRACTIONS AND RANDOM CONTINUED FRACTIONS 325 4.6.3 BERNOULLI INNOVATION
330 4.7 NONNEGATIVITY CONSTRAINTS 336 4.8 A MODEL WITH MULTIPLICATIVE
SHOCKS, AND THE SURVIVAL PROBABILITY OF AN ECONOMIC AGENT 338 4.9
COMPLEMENTS AND DETAILS 342 5 INVARIANT DISTRIBUTIONS: ESTIMATION AND
COMPUTATION 349 5.1 INTRODUCTION 349 5.2 ESTIMATING THE INVARIANT
DISTRIBUTION 350 5.3 A SUFFICIENT CONDITION FOR V^-CONSISTENCY 351 5.3.1
YTZ-CONSISTENCY 352 5.4 CENTRAL LIMIT THEOREMS 360 5.5 THE NATURE OF THE
INVARIANT DISTRIBUTION 365 5.5.1 RANDOM ITERATIONS OF TWO QUADRATIC MAPS
367 5.6 COMPLEMENTS AND DETAILS 369 5.7 SUPPLEMENTARY EXERCISES 375 6
DISCOUNTED DYNAMIC PROGRAMMING UNDER UNCERTAINTY 379 6.1 INTRODUCTION
379 6.2 THE MODEL 380 6.2.1 OPTIMALITY AND THE FUNCTIONAL EQUATION OF
DYNAMIC PROGRAMMING 381 VIII CONTENTS 6.3 THE MAXIMUM THEOREM: A
DIGRESSION 6.3.1 CONTINUOUS CORRESPONDENCES 63.2 THE MAXIMUM THEOREM AND
THE EXISTENCE OF A MEASURABLE SELECTION 6.4 DYNAMIC PROGRAMMING WITH A
COMPACT ACTION SPACE 6.5 APPLICATIONS 6.5.1 THE AGGREGATIVE MODEL OF
OPTIMAL GROWTH UNDER UNCERTAINTY: THE DISCOUNTED CASE 6.5.2 INTERIOR
OPTIMAL PROCESSES 6.5.3 THE RANDOM DYNAMICAL SYSTEM OF OPTIMAL INPUTS
6.5.4 AC CUMUL ATION OF RI SKY C AP ITAL 6.6 COMPLEMENTS AND DETAILS
6.6.1 UPPER SEMICONTINUOUS MODEL 6.6.2 THE CONTROLLED SEMI-MARKOV MODEL
6.6.3 STATE-DEPENDENT ACTIONS ^ APPENDIX AL. METRIC SPACES:
SEPARABILITY, COMPLETENESS, AND COMPACTNESS A 1.1. SEPARABILITY AL,2,
COMPLETENESS A1.3. COMPACTNESS A2. INFINITE PRODUCTS OF METRIC SPACES
AND THE DIAGONALIZATION ARGUMENT A3. MEASURABILITY A3.1. SUBSPACES A3.2.
PRODUCT SPACES; SEPARABILITY ONCE AGAIN A3.3. THE SUPPORT OF A MEASURE
A3,4. CHANGE OF VARIABLE A4. BOREL-CANTELLI LEMMA A5. CONVERGENCE
BIBLIOGRAPHY AUTHOR INDEX SUBJECT INDEX 385 385 386 388 390 390 397 402
407 409 409 410 415 419 419 420 420 422 423 425 426 426 428 428 430 431
435 453 457 |
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| author | Bhattacharya, Rabindra N. 1937- Majumdar, Mukul 1944- |
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| author_role | aut aut |
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| dewey-full | 515/.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.39 |
| dewey-sort | 3515 239 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
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| id | DE-604.BV022545645 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:11:48Z |
| indexdate | 2024-07-09T20:59:56Z |
| institution | BVB |
| isbn | 9780521825658 0521825652 9780521532723 0521532728 |
| language | English |
| lccn | 006024380 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015752024 |
| oclc_num | 70823127 |
| open_access_boolean | |
| owner | DE-29T DE-1051 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-188 DE-11 |
| owner_facet | DE-29T DE-1051 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-188 DE-11 |
| physical | XV, 463 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Bhattacharya, Rabindra N. 1937- Verfasser (DE-588)120600188 aut Random dynamical systems theory and applications Rabi Bhattacharya ; Mukul Majumdar 1. publ. Cambridge, Mass.[u.a.] Cambridge Univ. Press 2007 XV, 463 S. txt rdacontent n rdamedia nc rdacarrier Dynamische systemen gtt Systèmes dynamiques aléatoires Random dynamical systems 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 Stochastischer Prozess (DE-588)4057630-9 s DE-604 Majumdar, Mukul 1944- Verfasser (DE-588)121897036 aut http://www.loc.gov/catdir/toc/ecip0618/2006024380.html Inhaltsverzeichnis http://www.loc.gov/catdir/enhancements/fy0729/2006024380-b.html Beschreibung für Leser SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015752024&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bhattacharya, Rabindra N. 1937- Majumdar, Mukul 1944- Random dynamical systems theory and applications Dynamische systemen gtt Systèmes dynamiques aléatoires Random dynamical systems Stochastischer Prozess (DE-588)4057630-9 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4013396-5 |
| title | Random dynamical systems theory and applications |
| title_auth | Random dynamical systems theory and applications |
| title_exact_search | Random dynamical systems theory and applications |
| title_exact_search_txtP | Random dynamical systems theory and applications |
| title_full | Random dynamical systems theory and applications Rabi Bhattacharya ; Mukul Majumdar |
| title_fullStr | Random dynamical systems theory and applications Rabi Bhattacharya ; Mukul Majumdar |
| title_full_unstemmed | Random dynamical systems theory and applications Rabi Bhattacharya ; Mukul Majumdar |
| title_short | Random dynamical systems |
| title_sort | random dynamical systems theory and applications |
| title_sub | theory and applications |
| topic | Dynamische systemen gtt Systèmes dynamiques aléatoires Random dynamical systems Stochastischer Prozess (DE-588)4057630-9 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dynamische systemen Systèmes dynamiques aléatoires Random dynamical systems Stochastischer Prozess Dynamisches System |
| url | http://www.loc.gov/catdir/toc/ecip0618/2006024380.html http://www.loc.gov/catdir/enhancements/fy0729/2006024380-b.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015752024&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bhattacharyarabindran randomdynamicalsystemstheoryandapplications AT majumdarmukul randomdynamicalsystemstheoryandapplications |
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