Special functions, probability semigroups, and Hamiltonian flows:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1978
|
| Schriftenreihe: | Lecture notes in mathematics
696 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 112 S. |
| ISBN: | 3540091009 0387091009 |
Internformat
MARC
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| 100 | 1 | |a Feinsilver, Philip J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Special functions, probability semigroups, and Hamiltonian flows |c Philip J. Feinsilver |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1978 | |
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| 490 | 1 | |a Lecture notes in mathematics |v 696 | |
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| 650 | 4 | |a Semigroups | |
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Datensatz im Suchindex
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| adam_text | TABLE OF CONTENTS
Page
Chapter I. Introduction. 1
Part 1. Analytical and Probabilistic Basis. 3
Chapter II. Basic Operator Theory. 3
Functional Calculus 3
Exponentials 3
Heisenberg Group Formulation 4
The Operator xD 6
Hamiltonian Formulation 6
Some Contours 7
Chapter III. Moment Theory. 8
The Operator C 8
Moment Polynomials 8
Functions with Negative Index 10
Vacuum Functions 10
Canonical Vacuums for H = L(z) 11
Differential and Integral Representations 13
Inversion Formula 14
Expansions in Terms of h s 14
Reproducing Kernel 15
The Flow for A 16
Application to the Integral of a Process 16
Some Aspects of Physical Significance 17
Examples of Moment Theory 18
Chapter IV. Orthogonal Theory. 22
Bernoulli Generators 22
Canonical Forms 23
Representations of J 25
Expansions 26
Generalized Rodrigues Formula 26
Data for Jn s: Recurrence Formula, Value of jR 28
Reproducing Kernel and Associated Kernel 29
Canonical Variables 31
Appendix: Summary of Notation Used for Parameters 34
General Forms 34
Chapter V. The Standard Processes. Exauples. 35
The Bernoulli Process 35
The Symmetric Bernoulli Process 39
The Exponential Process 41
The Poisson Process 45
Brownian Motion 49
Canonical Moments 51
VI
Chapter V, continued.
Scalings 52
Summary of Forms 52
Lagrangians 53
Part 2. Further Probabilistic Aspects. 55
Chapter VI. Limit Theorems. 55
Chapter VII. Discrete Theory, Martingales, Stochastic
Integrals. 63
Iterated Integration and Exponentials 63
Discrete Iterated Integrals 64
Martingales and Martingale Differences 65
Processes with Independent Increments 66
Deterministic Examples 67
Further Remarks 69
Basic Operators 69
Probabilistic Theory 71
Part 3. Extensions. 77
Chapter VIII. Multidimensional Theory. 77
Moment Theory 77
Independent Processes 79
Radial and angular Variables 82
Some Simple Invariance Properties 83
Orthogonal Theory 85
Examples 88
Canonical Variables 90
Further Remarks. Recursion Formulas 91
Some Remarks on the General Bernoulli Generator 96
Lagrangians 97
Chapter IX. Hamiltonian Processes and Stochastic Processes. 98
analytical Martingales 98
Functionals of Processes 100
The Feynman-Kac Formula 101
Chapter X. Concluding Remarks. 107
Bibliography 109
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:52Z |
| institution | BVB |
| isbn | 3540091009 0387091009 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001482551 |
| oclc_num | 4492551 |
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| physical | VI, 112 S. |
| publishDate | 1978 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Feinsilver, Philip J. Verfasser aut Special functions, probability semigroups, and Hamiltonian flows Philip J. Feinsilver Berlin [u.a.] Springer 1978 VI, 112 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 696 Fonctions spéciales Hamiltonianen gtt Probabilités Semi-groupes Speciale functies (wiskunde) gtt Systèmes hamiltoniens Functions, Special Hamiltonian systems Probabilities Semigroups Spezielle Funktion (DE-588)4182213-4 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Spezielle Funktion (DE-588)4182213-4 s DE-604 Distribution Funktionalanalysis (DE-588)4070505-5 s Stochastisches Integral (DE-588)4126478-2 s Lecture notes in mathematics 696 (DE-604)BV000676446 696 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001482551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Feinsilver, Philip J. Special functions, probability semigroups, and Hamiltonian flows Lecture notes in mathematics Fonctions spéciales Hamiltonianen gtt Probabilités Semi-groupes Speciale functies (wiskunde) gtt Systèmes hamiltoniens Functions, Special Hamiltonian systems Probabilities Semigroups Spezielle Funktion (DE-588)4182213-4 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| subject_GND | (DE-588)4182213-4 (DE-588)4070505-5 (DE-588)4126478-2 |
| title | Special functions, probability semigroups, and Hamiltonian flows |
| title_auth | Special functions, probability semigroups, and Hamiltonian flows |
| title_exact_search | Special functions, probability semigroups, and Hamiltonian flows |
| title_full | Special functions, probability semigroups, and Hamiltonian flows Philip J. Feinsilver |
| title_fullStr | Special functions, probability semigroups, and Hamiltonian flows Philip J. Feinsilver |
| title_full_unstemmed | Special functions, probability semigroups, and Hamiltonian flows Philip J. Feinsilver |
| title_short | Special functions, probability semigroups, and Hamiltonian flows |
| title_sort | special functions probability semigroups and hamiltonian flows |
| topic | Fonctions spéciales Hamiltonianen gtt Probabilités Semi-groupes Speciale functies (wiskunde) gtt Systèmes hamiltoniens Functions, Special Hamiltonian systems Probabilities Semigroups Spezielle Funktion (DE-588)4182213-4 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| topic_facet | Fonctions spéciales Hamiltonianen Probabilités Semi-groupes Speciale functies (wiskunde) Systèmes hamiltoniens Functions, Special Hamiltonian systems Probabilities Semigroups Spezielle Funktion Distribution Funktionalanalysis Stochastisches Integral |
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