Stochastic processes and orthogonal polynomials:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2000
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| Schriftenreihe: | Lecture notes in statistics
146 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 163 S. graph. Darst. |
| ISBN: | 038795015X |
Internformat
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| 245 | 1 | 0 | |a Stochastic processes and orthogonal polynomials |c Wim Schoutens |
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| 650 | 4 | |a Polynômes orthogonaux | |
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| 650 | 4 | |a Processus stochastiques | |
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Datensatz im Suchindex
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| adam_text | WIM SCHOUTENS STOCHASTIC PROCESSES AND ORTHOGONAL POLYNOMIALS SPRINGER
CONTENTS PREFACE VII 1 THE ASKEY SCHEME OF ORTHOGONAL POLYNOMIALS 1 1.1
PRELIMINARIES 1 1.2 ORTHOGONAL POLYNOMIALS 3 1.2.1 ORTHOGONALITY
RELATIONS 3 1.2.2 THREE-TERM RECURRENCE RELATION 3 1.3 CLASSICAL
ORTHOGONAL POLYNOMIALS 4 1.3.1 HYPERGEOMETRIC TYPE EQUATIONS 4 1.3.2
CLASSIFICATION OF CLASSICAL ORTHOGONAL POLYNOMIALS . 6 1.4 THE ASKEY
SCHEME 10 2 STOCHASTIC PROCESSES 15 2.1 MARKOV PROCESSES 15 2.2 MARKOV
CHAINS 17 2.3 RANDOM WALKS 18 2.4 BIRTH AND DEATH PROCESSES 19 2.5 LEVY
PROCESSES 22 2.6 DIFFUSION PROCESSES 24 2.6.1 CALCULATION OF TRANSITION
PROBABILITIES . 25 2.6.2 EXAMPLES 27 3 BIRTH AND DEATH PROCESSES, RANDOM
WALKS, AND ORTHOGO- NAL POLYNOMIALS 31 XII CONTENTS 3.1 KARLIN AND
MCGREGOR SPECTRAL REPRESENTATION FOR BIRTH AND DEATH PROCESSES 32 3.2
LIMITING CONDITIONAL DISTRIBUTIONS FOR BIRTH AND DEATH PRO- CESSES 36
3.2.1 ABSORBING CASE . 36 3.2.2 REFLECTING CASE 39 3.3 KARLIN AND
MCGREGOR SPECTRAL REPRESENTATION FOR RANDOM WALKS 41 3.4 LIMITING
CONDITIONAL DISTRIBUTIONS FOR RANDOM WALKS ... 42 4 SHEFFER SYSTEMS 45
4.1 LEVY-SHEFFER SYSTEMS 45 4.2 SHEFFER SETS AND ORTHOGONALITY 48 4.3
THE LEVY-MEIXNER SYSTEMS 51 4.3.1 BROWNIAN MOTION-HERMITE 52 4.3.2
POISSON PROCESS-CHARLIER 53 4.3.3 GAMMA PROCESS-LAGUERRE 54 4.3.4 PASCAL
PROCESS-MEIXNER 55 4.3.5 MEIXNER PROCESS-MEIXNER-POLLACZEK 56 4.4 I.I.D.
SHEFFER SYSTEMS 58 4.4.1 EXAMPLES 59 4.5 CONVOLUTION RELATIONS 61 5
ORTHOGONAL POLYNOMIALS IN STOCHASTIC INTEGRATION THEORY 63 5.1
INTRODUCTION 64 5.2 STOCHASTIC INTEGRATION WITH RESPECT TO THE POISSON
PROCESS 65 5.3 STOCHASTIC SUMMATION WITH RESPECT TO THE BINOMIAL PROCESS
68 5.4 CHAOTIC AND PREDICTABLE REPRESENTATIONS FOR LEVY PROCESSES 70
5.4.1 CHAOTIC AND PREDICTABLE REPRESENTATION PROPERTY . . 70 5.4.2 POWER
JUMP PROCESSES AND TEUGELS MARTINGALES ... 72 5.4.3 STRONG
ORTHOGONALIZATION OF THE TEUGELS MARTINGALES 73 5.4.4 REPRESENTATION
PROPERTIES 75 5.5 EXAMPLES 83 5.5.1 THE GAMMA PROCESS 83 5.5.2 THE
PASCAL PROCESS 85 5.5.3 THE MEIXNER PROCESS 86 5.5.4 BROWNIAN-GAMMA
PROCESS 86 6 STEIN APPROXIMATION AND ORTHOGONAL POLYNOMIALS 91 6.1
STEIN S METHOD 91 6.1.1 STANDARD NORMAL DISTRIBUTION 91 6.1.2 POISSON
DISTRIBUTION 94 6.1.3 GENERAL PROCEDURE 94 6.2 THE GENERATOR METHOD 95
6.3 STEIN OPERATORS 96 CONTENTS XIII 6.4 STEIN S METHOD FOR PEARSON AND
ORD FAMILIES 97 6.4.1 THE PEARSON FAMILY OF CONTINUOUS DISTRIBUTIONS . .
97 6.4.2 ORD S FAMILY OF DISCRETE DISTRIBUTIONS 105 6.4.3 ORTHOGONAL
POLYNOMIALS 113 6.4.4 MARKOV PROCESS 114 CONCLUSION 123 A DISTRIBUTIONS
127 B TABLES OF CLASSICAL ORTHOGONAL POLYNOMIALS 129 B.L HERMITE
POLYNOMIALS AND THE NORMAL DISTRIBUTION 130 B.2 SCALED HERMITE
POLYNOMIALS AND THE STANDARD NORMAL DIS- TRIBUTION 131 B.3 HERMITE
POLYNOMIALS WITH PARAMETER AND THE NORMAL DIS- TRIBUTION 132 B.4
CHARLIER POLYNOMIALS AND THE POISSON DISTRIBUTION 133 B.5 LAGUERRE
POLYNOMIALS AND THE GAMMA DISTRIBUTION 134 B.6 MEIXNER POLYNOMIALS AND
THE PASCAL DISTRIBUTION 135 B.7 KRAWTCHOUK POLYNOMIALS AND THE BINOMIAL
DISTRIBUTION . . 136 B.8 JACOBI POLYNOMIALS AND THE BETA KERNEL 137 B.9
HAHN POLYNOMIALS AND THE HYPERGEOMETRIC DISTRIBUTION . . 138 C TABLE OF
DUALITY RELATIONS BETWEEN CLASSICAL ORTHOGONAL POLYNOMIALS 139 D TABLES
OF SHEFFER SYSTEMS 141 D.L SHEFFER POLYNOMIALS AND THEIR GENERATING
FUNCTIONS . . . . 142 D.2 SHEFFER POLYNOMIALS AND THEIR ASSOCIATED
DISTRIBUTIONS . . 143 D.3 MARTINGALE RELATIONS WITH SHEFFER POLYNOMIALS
144 E TABLES OF LIMIT RELATIONS BETWEEN ORTHOGONAL POLYNOMIALS IN THE
ASKEY SCHEINE 145 REFERENCES 149 INDEX 159
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:41:50Z |
| institution | BVB |
| isbn | 038795015X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009005131 |
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| physical | XIII, 163 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Schoutens, Wim Verfasser aut Stochastic processes and orthogonal polynomials Wim Schoutens New York [u.a.] Springer 2000 XIII, 163 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 146 Orthogonale reeksen gtt Polynômes orthogonaux Polynômes orthogonaux ram Processus stochastiques Processus stochastiques ram Stochastische processen gtt Orthogonal polynomials Stochastic processes Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Orthogonale Polynome (DE-588)4172863-4 s DE-604 Lecture notes in statistics 146 (DE-604)BV002447846 146 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009005131&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schoutens, Wim Stochastic processes and orthogonal polynomials Lecture notes in statistics Orthogonale reeksen gtt Polynômes orthogonaux Polynômes orthogonaux ram Processus stochastiques Processus stochastiques ram Stochastische processen gtt Orthogonal polynomials Stochastic processes Orthogonale Polynome (DE-588)4172863-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4172863-4 (DE-588)4057630-9 |
| title | Stochastic processes and orthogonal polynomials |
| title_auth | Stochastic processes and orthogonal polynomials |
| title_exact_search | Stochastic processes and orthogonal polynomials |
| title_full | Stochastic processes and orthogonal polynomials Wim Schoutens |
| title_fullStr | Stochastic processes and orthogonal polynomials Wim Schoutens |
| title_full_unstemmed | Stochastic processes and orthogonal polynomials Wim Schoutens |
| title_short | Stochastic processes and orthogonal polynomials |
| title_sort | stochastic processes and orthogonal polynomials |
| topic | Orthogonale reeksen gtt Polynômes orthogonaux Polynômes orthogonaux ram Processus stochastiques Processus stochastiques ram Stochastische processen gtt Orthogonal polynomials Stochastic processes Orthogonale Polynome (DE-588)4172863-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Orthogonale reeksen Polynômes orthogonaux Processus stochastiques Stochastische processen Orthogonal polynomials Stochastic processes Orthogonale Polynome Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009005131&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002447846 |
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