Gaussian processes:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Japanese |
| Published: |
Providence, RI
American Mathemat. Soc.
2007
|
| Edition: | Reprint. |
| Series: | Translations of mathematical monographs
120 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Japan. übers. |
| Physical Description: | XV, 183 S. graph. Darst. |
| ISBN: | 0821843583 9780821843581 |
Staff View
MARC
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| 264 | 1 | |a Providence, RI |b American Mathemat. Soc. |c 2007 | |
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Record in the Search Index
| _version_ | 1804137996981633025 |
|---|---|
| adam_text | Contents
Preface
to the English Edition
vii
Preface
ix
Introduction
xi
Chapter I. Foundations of Probability Theory and Limit Theorems
1
§1.
Probability spaces and random variables
1
§2.
Probability distributions of random variables (random vectors)
and characteristic functions
3
§3.
Convergence of sequences of random variables
6
§4.
Limit theorems for sums of independent random variables
7
§5.
Conditional expectations and martingales
8
§6.
Measures on function spaces (measures induced from
stochastic processes)
12
Chapter II. Systems of Gaussian Random Variables
15
§ 1.
Definitions and preliminaries
15
§2.
Some important properties of a Gaussian system
17
§3.
Complex Gaussian systems
21
§4.
Discrete parameter Gaussian processes: Canonical
representation
23
§5.
Continuous parameter Gaussian processes: Brownian motion
31
Chapter III. Stationary Gaussian Processes and Their Representations
37
§1.
Discrete parameter stationary processes
37
§2.
Spectral representation of a stationary Gaussian process
42
§3.
Canonical representation of stationary processes I: The discrete
parameter case
46
§4.
Canonical representation of stationary processes II: The
continuous parameter case
52
Chapter IV. Canonical Representation of Gaussian Processes: General
Theory and Multiplicity
55
§1.
Propagation of random phenomena
55
§2.
Canonical representation and multiplicity
57
vi
CONTENTS
§3.
Gaussian processes and reproducing kernel Hubert spaces
66
§4.
Examples of a canonical representation and a noncanonical one
70
§5.
Application to prediction theory
74
Chapter V. Multiple Markov Gaussian Processes
79
§1.
Multiple Markov processes with discrete parameter
80
§2.
Multiple Markov Gaussian processes with continuous
parameter
83
§3.
Multiple Markov Gaussian processes in the restricted sense
89
§4.
Multiple Markov stationary Gaussian processes
100
§5.
Levy s MiO-process
107
§6.
r-positivity
116
Chapter VI. Equivalence of Gaussian Processes
121
§ 1.
Setting up the problem
121
§2.
General theory of equivalence of Gaussian measures
122
§3.
Equivalence of Gaussian processes with discrete parameter
128
§4.
Canonical representations of Gaussian processes equivalent to
Wiener processes
131
§5.
Canonical representation of Gaussian processes equivalent to a
given Gaussian process
141
§6.
Constructing innovation processes
143
Appendix. Stochastic Integrals and Martingales
149
§ 1.
Multiple Wiener integrals
149
§2.
Martingales and stochastic
(Ito)
integrals
156
§3.
Itô s
formula and Girsanov s theorem
165
Historical Notes
171
References
177
Subject Index
181
|
| adam_txt |
Contents
Preface
to the English Edition
vii
Preface
ix
Introduction
xi
Chapter I. Foundations of Probability Theory and Limit Theorems
1
§1.
Probability spaces and random variables
1
§2.
Probability distributions of random variables (random vectors)
and characteristic functions
3
§3.
Convergence of sequences of random variables
6
§4.
Limit theorems for sums of independent random variables
7
§5.
Conditional expectations and martingales
8
§6.
Measures on function spaces (measures induced from
stochastic processes)
12
Chapter II. Systems of Gaussian Random Variables
15
§ 1.
Definitions and preliminaries
15
§2.
Some important properties of a Gaussian system
17
§3.
Complex Gaussian systems
21
§4.
Discrete parameter Gaussian processes: Canonical
representation
23
§5.
Continuous parameter Gaussian processes: Brownian motion
31
Chapter III. Stationary Gaussian Processes and Their Representations
37
§1.
Discrete parameter stationary processes
37
§2.
Spectral representation of a stationary Gaussian process
42
§3.
Canonical representation of stationary processes I: The discrete
parameter case
46
§4.
Canonical representation of stationary processes II: The
continuous parameter case
52
Chapter IV. Canonical Representation of Gaussian Processes: General
Theory and Multiplicity
55
§1.
Propagation of random phenomena
55
§2.
Canonical representation and multiplicity
57
vi
CONTENTS
§3.
Gaussian processes and reproducing kernel Hubert spaces
66
§4.
Examples of a canonical representation and a noncanonical one
70
§5.
Application to prediction theory
74
Chapter V. Multiple Markov Gaussian Processes
79
§1.
Multiple Markov processes with discrete parameter
80
§2.
Multiple Markov Gaussian processes with continuous
parameter
83
§3.
Multiple Markov Gaussian processes in the restricted sense
89
§4.
Multiple Markov stationary Gaussian processes
100
§5.
Levy's MiO-process
107
§6.
r-positivity
116
Chapter VI. Equivalence of Gaussian Processes
121
§ 1.
Setting up the problem
121
§2.
General theory of equivalence of Gaussian measures
122
§3.
Equivalence of Gaussian processes with discrete parameter
128
§4.
Canonical representations of Gaussian processes equivalent to
Wiener processes
131
§5.
Canonical representation of Gaussian processes equivalent to a
given Gaussian process
141
§6.
Constructing innovation processes
143
Appendix. Stochastic Integrals and Martingales
149
§ 1.
Multiple Wiener integrals
149
§2.
Martingales and stochastic
(Ito)
integrals
156
§3.
Itô's
formula and Girsanov's theorem
165
Historical Notes
171
References
177
Subject Index
181 |
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| author | Hida, Takeyuki 1927-2017 Hitsuda, Masuyuki |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Reprint. |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T21:58:12Z |
| indexdate | 2024-07-09T21:21:10Z |
| institution | BVB |
| isbn | 0821843583 9780821843581 |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016723745 |
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| physical | XV, 183 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | American Mathemat. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Hida, Takeyuki 1927-2017 Verfasser (DE-588)124605257 aut Gausu-katei Gaussian processes Takeyuki Hida ; Masuyuki Hitsuda Reprint. Providence, RI American Mathemat. Soc. 2007 XV, 183 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 120 Aus d. Japan. übers. Gaussian processes Gauß-Prozess (DE-588)4156111-9 gnd rswk-swf Gauß-Prozess (DE-588)4156111-9 s DE-604 Hitsuda, Masuyuki Verfasser aut Translations of mathematical monographs 120 (DE-604)BV000002394 120 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016723745&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hida, Takeyuki 1927-2017 Hitsuda, Masuyuki Gaussian processes Translations of mathematical monographs Gaussian processes Gauß-Prozess (DE-588)4156111-9 gnd |
| subject_GND | (DE-588)4156111-9 |
| title | Gaussian processes |
| title_alt | Gausu-katei |
| title_auth | Gaussian processes |
| title_exact_search | Gaussian processes |
| title_exact_search_txtP | Gaussian processes |
| title_full | Gaussian processes Takeyuki Hida ; Masuyuki Hitsuda |
| title_fullStr | Gaussian processes Takeyuki Hida ; Masuyuki Hitsuda |
| title_full_unstemmed | Gaussian processes Takeyuki Hida ; Masuyuki Hitsuda |
| title_short | Gaussian processes |
| title_sort | gaussian processes |
| topic | Gaussian processes Gauß-Prozess (DE-588)4156111-9 gnd |
| topic_facet | Gaussian processes Gauß-Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016723745&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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