Essentials of stochastic processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Japanese |
| Published: |
Providence, RI
American Mathematical Society
2006
|
| Series: | Translations of mathematical monographs
231 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 171 Seiten 27 cm |
| ISBN: | 0821838989 9780821838983 |
Staff View
MARC
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| 240 | 1 | 0 | |a Kakuritsu katei |
| 245 | 1 | 0 | |a Essentials of stochastic processes |c Kiyosi Itô. Translated by Yuji Ito |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2006 | |
| 300 | |a x, 171 Seiten |c 27 cm | ||
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Record in the Search Index
| _version_ | 1804138011530625024 |
|---|---|
| adam_text | Contents
Author s Preface
vii
Translator s Foreword
ix
Chapter
1.
Basic Concepts
1
1.1.
Measure Theoretic Probability
(1)
Intuitive Background
1
1.2.
Probability Distribution
3
1.3.
Measure Theoretic Probability
(2)
Mathematical Structure
6
1.4.
Distribution Function, Characteristic Function, Mean, Variance
8
1.5.
Stochastic Process
13
Chapter
2.
Additive Processes
15
2.1.
Definition of Additive Process
15
2.2.
Examples of Additive Processes
16
2.3.
Inequalities Concerning Sums of Independent Random Variables
17
2.4. 0-1
Law
19
2.5.
Convergence of Additive Sequences
21
2.6.
Dispersion
24
2.7.
Simple Properties of Additive Processes
28
2.8.
Separability of Stochastic Processes
32
2.9.
Separable
Poisson
Processes
33
2.10.
Separable Wiener Processes
36
2.11.
Additive Processes Continuous in Probability and Infinitely Divisible
Distributions
39
2.12.
Structure of Separable Additive Processes Continuous in Probability
43
2.13.
Canonical Form of Infinitely Divisible Distributions
44
2.14.
Various Methods for Construction of
Poisson
Processes
47
2.15.
Compound
Poisson
Processes
49
2.16.
Stable Distributions and Stable Processes
50
Chapter
3.
Stationary Processes
57
3.1.
Definition of Stationary Process
57
3.2.
Preliminary Material Related to Investigations of Stationary Processes
58
3.3.
Spectral Decomposition of Weakly Stationary Processes
60
3.4.
Spectral Decomposition of Sample Processes of Weakly Stationary
Processes
62
3.5.
Ergodic Theorem Concerning Strongly Stationary Processes
64
3.6.
Complex Normal System
67
3.7.
Normal Stationary Processes
71
3.8.
Wiener Integrals and Multiple Wiener Integrals
73
vi
CONTENTS
3.9.
Ergodicity
of Normal Stationary Processes
74
3.10.
Generalizations of Stationary Processes
77
Chapter
4.
Markov Processes
85
4.1.
Conditional Probability
85
4.2.
Conditional Expectation
86
4.3.
Martingales
88
4.4.
Transition Probabilities
88
4.5.
Semi-Groups and Dual Semi-Groups Associated with Transition
Probabilities
90
4.6.
Hille-Yosida Theory (i)
92
4.7.
Hille-Yosida Theory (ii). Construction of Semi-Group
95
4.8.
Generators of Transition Probabilities (i). General Theory
98
4.9.
Generators of Transition Probabilities (ii). Examples
101
4.10.
Markov Processes (i). Markov Property
104
4.11.
Markov Processes (ii). Properties of Sample Processes
106
4.12.
Markov Processes
(iii).
Strong Markov Property
108
4.13.
Markov Times
112
4.14.
Dynkin s Theorem on Generators
115
4.15.
Examples of Markov Processes
117
4.16.
Temporally Homogeneous Additive Processes
120
4.17.
Birth and Death Processes
121
Chapter
5.
Diffusion
127
5.1.
Diffusive Points
127
5.2.
Ray s Theorem
127
5.3.
Local Generators
130
5.4.
Classification of One-Dimensional Diffusive Points
132
5.5.
Feller s Canonical Scale
134
5.6.
Feller s Canonical Measure
138
5.7.
Feller s Canonical Form
139
5.8.
Local Generators at Generalized Shunts
143
5.9.
Distribution of the First Passage Time
145
5.10.
Classical Diffusion Processes
148
5.11.
Classification of Boundary Points with Respect to Feller s Operator
DmD+
151
5.12.
Particular Solutions of the Homogeneous Equation (X — DmDf)u
— 0
(λ
> 0) 153
5.13.
General Solutions of the Homogeneous Equation
(λ
—
DmDf)u
= 0
(λ
> 0) 155
5.14.
Solutions of the Non-Homogeneous Equation
(λ
-
DmDf)g
= ƒ 159
5.15.
Distributions of Various Quantities Associated with x^a t) in a
Regular Interval
162
5.16.
Behavior of a Process at the Boundaries of a Regular Interval
164
Postscript
169
|
| adam_txt |
Contents
Author's Preface
vii
Translator's Foreword
ix
Chapter
1.
Basic Concepts
1
1.1.
Measure Theoretic Probability
(1)
Intuitive Background
1
1.2.
Probability Distribution
3
1.3.
Measure Theoretic Probability
(2)
Mathematical Structure
6
1.4.
Distribution Function, Characteristic Function, Mean, Variance
8
1.5.
Stochastic Process
13
Chapter
2.
Additive Processes
15
2.1.
Definition of Additive Process
15
2.2.
Examples of Additive Processes
16
2.3.
Inequalities Concerning Sums of Independent Random Variables
17
2.4. 0-1
Law
19
2.5.
Convergence of Additive Sequences
21
2.6.
Dispersion
24
2.7.
Simple Properties of Additive Processes
28
2.8.
Separability of Stochastic Processes
32
2.9.
Separable
Poisson
Processes
33
2.10.
Separable Wiener Processes
36
2.11.
Additive Processes Continuous in Probability and Infinitely Divisible
Distributions
39
2.12.
Structure of Separable Additive Processes Continuous in Probability
43
2.13.
Canonical Form of Infinitely Divisible Distributions
44
2.14.
Various Methods for Construction of
Poisson
Processes
47
2.15.
Compound
Poisson
Processes
49
2.16.
Stable Distributions and Stable Processes
50
Chapter
3.
Stationary Processes
57
3.1.
Definition of Stationary Process
57
3.2.
Preliminary Material Related to Investigations of Stationary Processes
58
3.3.
Spectral Decomposition of Weakly Stationary Processes
60
3.4.
Spectral Decomposition of Sample Processes of Weakly Stationary
Processes
62
3.5.
Ergodic Theorem Concerning Strongly Stationary Processes
64
3.6.
Complex Normal System
67
3.7.
Normal Stationary Processes
71
3.8.
Wiener Integrals and Multiple Wiener Integrals
73
vi
CONTENTS
3.9.
Ergodicity
of Normal Stationary Processes
74
3.10.
Generalizations of Stationary Processes
77
Chapter
4.
Markov Processes
85
4.1.
Conditional Probability
85
4.2.
Conditional Expectation
86
4.3.
Martingales
88
4.4.
Transition Probabilities
88
4.5.
Semi-Groups and Dual Semi-Groups Associated with Transition
Probabilities
90
4.6.
Hille-Yosida Theory (i)
92
4.7.
Hille-Yosida Theory (ii). Construction of Semi-Group
95
4.8.
Generators of Transition Probabilities (i). General Theory
98
4.9.
Generators of Transition Probabilities (ii). Examples
101
4.10.
Markov Processes (i). Markov Property
104
4.11.
Markov Processes (ii). Properties of Sample Processes
106
4.12.
Markov Processes
(iii).
Strong Markov Property
108
4.13.
Markov Times
112
4.14.
Dynkin's Theorem on Generators
115
4.15.
Examples of Markov Processes
117
4.16.
Temporally Homogeneous Additive Processes
120
4.17.
Birth and Death Processes
121
Chapter
5.
Diffusion
127
5.1.
Diffusive Points
127
5.2.
Ray's Theorem
127
5.3.
Local Generators
130
5.4.
Classification of One-Dimensional Diffusive Points
132
5.5.
Feller's Canonical Scale
134
5.6.
Feller's Canonical Measure
138
5.7.
Feller's Canonical Form
139
5.8.
Local Generators at Generalized Shunts
143
5.9.
Distribution of the First Passage Time
145
5.10.
Classical Diffusion Processes
148
5.11.
Classification of Boundary Points with Respect to Feller's Operator
DmD+
151
5.12.
Particular Solutions of the Homogeneous Equation (X — DmDf)u
— 0
(λ
> 0) 153
5.13.
General Solutions of the Homogeneous Equation
(λ
—
DmDf)u
= 0
(λ
> 0) 155
5.14.
Solutions of the Non-Homogeneous Equation
(λ
-
DmDf)g
= ƒ 159
5.15.
Distributions of Various Quantities Associated with x^a\t) in a
Regular Interval
162
5.16.
Behavior of a Process at the Boundaries of a Regular Interval
164
Postscript
169 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Itō, Kiyoshi 1915-2008 |
| author_GND | (DE-588)119388073 |
| author_facet | Itō, Kiyoshi 1915-2008 |
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| ctrlnum | (OCoLC)475149191 (DE-599)BVBBV035065414 |
| dewey-full | 519.2 519.2/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 519.2/3 |
| dewey-search | 519.2 519.2/3 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV035065414 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:02:09Z |
| indexdate | 2024-07-09T21:21:24Z |
| institution | BVB |
| isbn | 0821838989 9780821838983 |
| language | English Japanese |
| lccn | 2006042673 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016733873 |
| oclc_num | 475149191 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-188 |
| physical | x, 171 Seiten 27 cm |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Itō, Kiyoshi 1915-2008 Verfasser (DE-588)119388073 aut Kakuritsu katei Essentials of stochastic processes Kiyosi Itô. Translated by Yuji Ito Providence, RI American Mathematical Society 2006 x, 171 Seiten 27 cm txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 231 Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 Translations of mathematical monographs 231 (DE-604)BV000002394 231 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016733873&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Itō, Kiyoshi 1915-2008 Essentials of stochastic processes Translations of mathematical monographs Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Essentials of stochastic processes |
| title_alt | Kakuritsu katei |
| title_auth | Essentials of stochastic processes |
| title_exact_search | Essentials of stochastic processes |
| title_exact_search_txtP | Essentials of stochastic processes |
| title_full | Essentials of stochastic processes Kiyosi Itô. Translated by Yuji Ito |
| title_fullStr | Essentials of stochastic processes Kiyosi Itô. Translated by Yuji Ito |
| title_full_unstemmed | Essentials of stochastic processes Kiyosi Itô. Translated by Yuji Ito |
| title_short | Essentials of stochastic processes |
| title_sort | essentials of stochastic processes |
| topic | Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastic processes Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016733873&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT itokiyoshi kakuritsukatei AT itokiyoshi essentialsofstochasticprocesses |