Chaos expansions, multiple Wiener-Itô integrals and their applications:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Boca Raton u.a.
CRC Press
1994
|
| Schriftenreihe: | Probability and stochastics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 377 S. |
| ISBN: | 0849380723 |
Internformat
MARC
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| 650 | 7 | |a Processus stochastiques |2 ram | |
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Datensatz im Suchindex
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| adam_text | Contents
1 Multiple Wiener ltd integrals: An introductory survey 1
Christian Houdrt, Victor Pfrez Abreu and Ali Slileyman Usttinel
1.1 Introduction 1
1.2 Multiple Wiener It6 integrals and chaos expansions 3
1.2.1 Introduction 3
1.2.2 Hu Meyer formula and continuous extensions 4
1.2.3 Different approaches and multiple integrals for other
processes 6
1.2.4 Chaos expansions 8
1.2.5 A survey of applications 9
1.2.6 Chaos expansions for other processes 11
1.3 Chaos random variables and processes 11
1.3.1 Introduction 11
1.3.2 Chaos random variables 12
1.3.3 Chaos stochastic processes 16
1.4 Anticipative stochastic calculus through chaos expansions ... 18
1.4.1 Stochastic integration for chaotic processes 19
1.4.2 Derivatives and Sobolev spaces of Wiener functionals . 20
1.4.3 Another approach to anticipative calculus 22
1.4.4 The Ornstein Uhlenbeck operator 23
2 The Hu Meyer formula. A view of the problem with special
attention to the Poisson case 35
Josep L. Soli and Frederic. Utzet
2.1 The Wiener case 35
2.2 The Poisson case 39
2.3 The Wiener and the Poisson cases again 40
2.4 New directions 43
3 Remarks on the existence of ^ traces 47
Gerald W. Johnson and Gopinath Kallianpur
3.1 Multiple Wiener Ito integrals and ^ traces 47
3.2 The existence of fc traces 51
3.2.1 L2([0,2tt]) 53
3.2.2 L2(R) 60
3.2.3 L2([0,oo)) 63
4 Multiple Wiener Ito integrals and a multivariate version of
Schoenberg s theorem 73
Olav Kallenberg
4.1 Schoenberg s theorem and rotatable arrays 73
4.2 Symmetries of multiple Wiener It6 integrals 75
4.3 Representations of rotatable CLRFs 78
4.4 Exchangeable random fields 82
5 The state of decoupling: A survey 87
Jerzy Szulga
5.1 Basic notions 87
5.1.1 Notation 88
5.1.2 A bit of history 90
5.1.3 Special classes of random variables 92
5.2 Decoupling in a quasi convex setting 100
5.2.1 Decoupling of homogeneous polynomials 101
5.2.2 The case of tails 103
5.2.3 Ramifications 104
5.2.4 Tetrahedral polynomials and geometry 110
5.2.5 Non zero diagonals 112
5.2.6 Multiple integrals 114
5.3 Other types of decoupling 114
5.3.1 Tangent processes and decoupling 114
5.3.2 Non integrable polynomials 116
5.3.3 Infinite order chaos 118
6 MWI expansions for functional; related to level crossing counts 125
Eric V. Slud
6.1 Introduction 125
6.2 Multiple Wiener It6 integral representations 128
6.3 Applications of the MWI expansion to crossing counts 133
6.3.1 Central limit theorems weak dependence case .... 133
6.3.2 Noncentral limit theorem 135
6.3.3 Crossings rates for mixed spectrum Gaussian signals . . 136
6.4 Generalized random functions related to crossings 138
7 Scaling limits of solutions of Burgers equation with singular
Gaussian initial data 145
Donatas Surgailis and Wojbor A. Woyczyriski
7.1 Preliminaries 145
7.2 Scaling limits 147
7.3 Spectra with discrete singularities 148
7.4 Spectra concentrated on lines 155
8 Weak convergence in dynamical systems to self similar
processes with time average representation 163
Michael T. Lacey
8.1 Introduction 163
8.2 Main results 165
8.3 r:z 2xmod 1 169
8.4 The general case 173
9 On exact tails for limiting distributions of U statistics in the
second Gaussian chaos 179
Peter Imkeller
9.1 Introduction 179
9.2 Notation and preliminaries 183
9.3 Positive tails 184
9.4 Negative tails 193
10 Limit theorems for empirical processes under dependence 205
Miguel A. Arcones and Bin Yu
10.1 Introduction 205
10.2 Empirical processes under mixing conditions 210
10.3 Empirical processes under long range dependence 211
10.4 The non central limit theorem for M estimators 215
11 Mixing for multiple Wiener Ito integral processes 223
Daniel W. Chambers
11.1 Introduction 223
11.2 Background 225
11.3 Results 228
12 Zero one laws for multiple stochastic integrals 233
Jan Rosiiiski and Gennady Samorodnitsky
12.1 Introduction and notation 233
12.2 A survey of zero one laws for infinitely divisible processes and
measures 237
12.3 A survey of 0 1 laws for multiple integrals and multilinear
forms 238
12.4 Zero one laws for sums of multiple Ldvy integrals under an
atomlessness assumption 240
12.5 Centering multiple stochastic integrals 246
12.6 Applications to sample path properties 254
13 Continuity of some Gaussian chaoses 261
Michael B. Marcus
13.1 Introduction and main result 261
14 Some formulas for anticipative Girsanov transformations 267
Jorge A. Le6n and Philip Protter
14.1 Introduction 267
14.2 Preliminaries 269
14.3 A result of Buckdahn interpreted through semimartingales . . . 270
14.4 An extension of Buckdahn s result 274
14.5 The unbounded case 282
14.6 A counterexample 288
15 Absolute continuity of processes and a derivation rule 293
Maria Emilia Caballero and Begona Ferndndez
15.1 Introduction 293
15.2 Preliminaries 294
15.3 Absolute continuity of processes 296
15.4 Properties of a stochastic equation 301
15.5 Applications 308
16 Smoothness of local time and related Wiener functionals 317
David Nualart and Josep Vives
16.1 Introduction 317
16.2 Sobolev spaces over the Wiener space 319
16.3 Smoothness of 6r(W(h)) using the Ornstein Uhlenbeck
semigroup 321
16.4 Smoothness of 6X(W( h)) using chaos expansions 322
16.5 Smoothness of Brownian local time 326
16.6 Smoothness of Brownian local time using chaos expansions . . 329
16.7 Smoothness of the renormalized autointersection local time of
the planar Brownian motion 331
17 Distributions on Wiener space and fluctuation limits of PoLsson
systems of Brownian bridges 337
Luis G. Gorostiza
17.1 Introduction 337
17.2 Notation and preliminaries 338
17.3 A nuclear Gelfand triple on Wiener space 340
17.4 Fluctuations of Poisson systems of Brownian bridges 341
18 Ito Ramer, Skorohod and Ogawa integrals with respect to
Gaussian processes and their interrelationship 349
Leszek Gawarecki and Vidyadhar Mandrekar
18.1 Introduction 349
18.2 Relation between Skorohod and Ogawa integrals 350
18.3 Ita Ramer integral 355
18.4 Relation between It6 Ramer, Ogawa and Skorohod integrals . . 362
18.5 Examples 364
|
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| dewey-raw | 519.2 |
| dewey-search | 519.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Konferenzschrift 1992 Guanajuato Stadt |
| id | DE-604.BV009794179 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:40:57Z |
| institution | BVB |
| isbn | 0849380723 |
| language | English |
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| physical | 377 S. |
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| series2 | Probability and stochastics series |
| spelling | Chaos expansions, multiple Wiener-Itô integrals and their applications ed. by Christian Houdré ... Boca Raton u.a. CRC Press 1994 377 S. txt rdacontent n rdamedia nc rdacarrier Probability and stochastics series Chaos (théorie des systèmes) ram Intégrales stochastiques ram Processus gaussiens ram Processus stochastiques ram Chaotic behavior in systems Gaussian processes Stochastic integrals Chaotisches System (DE-588)4316104-2 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Chaos (DE-588)4191419-3 gnd rswk-swf Wiener-Itô-Integral (DE-588)4189868-0 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1992 Guanajuato Stadt gnd-content Wiener-Itô-Integral (DE-588)4189868-0 s DE-604 Chaotisches System (DE-588)4316104-2 s Stochastischer Prozess (DE-588)4057630-9 s Chaos (DE-588)4191419-3 s 1\p DE-604 Stochastisches Integral (DE-588)4126478-2 s 2\p DE-604 Houdré, Christian 1959- Sonstige (DE-588)121699854 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006479201&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chaos expansions, multiple Wiener-Itô integrals and their applications Chaos (théorie des systèmes) ram Intégrales stochastiques ram Processus gaussiens ram Processus stochastiques ram Chaotic behavior in systems Gaussian processes Stochastic integrals Chaotisches System (DE-588)4316104-2 gnd Stochastisches Integral (DE-588)4126478-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Chaos (DE-588)4191419-3 gnd Wiener-Itô-Integral (DE-588)4189868-0 gnd |
| subject_GND | (DE-588)4316104-2 (DE-588)4126478-2 (DE-588)4057630-9 (DE-588)4191419-3 (DE-588)4189868-0 (DE-588)1071861417 |
| title | Chaos expansions, multiple Wiener-Itô integrals and their applications |
| title_auth | Chaos expansions, multiple Wiener-Itô integrals and their applications |
| title_exact_search | Chaos expansions, multiple Wiener-Itô integrals and their applications |
| title_full | Chaos expansions, multiple Wiener-Itô integrals and their applications ed. by Christian Houdré ... |
| title_fullStr | Chaos expansions, multiple Wiener-Itô integrals and their applications ed. by Christian Houdré ... |
| title_full_unstemmed | Chaos expansions, multiple Wiener-Itô integrals and their applications ed. by Christian Houdré ... |
| title_short | Chaos expansions, multiple Wiener-Itô integrals and their applications |
| title_sort | chaos expansions multiple wiener ito integrals and their applications |
| topic | Chaos (théorie des systèmes) ram Intégrales stochastiques ram Processus gaussiens ram Processus stochastiques ram Chaotic behavior in systems Gaussian processes Stochastic integrals Chaotisches System (DE-588)4316104-2 gnd Stochastisches Integral (DE-588)4126478-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Chaos (DE-588)4191419-3 gnd Wiener-Itô-Integral (DE-588)4189868-0 gnd |
| topic_facet | Chaos (théorie des systèmes) Intégrales stochastiques Processus gaussiens Processus stochastiques Chaotic behavior in systems Gaussian processes Stochastic integrals Chaotisches System Stochastisches Integral Stochastischer Prozess Chaos Wiener-Itô-Integral Konferenzschrift 1992 Guanajuato Stadt |
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