Stochastic differential equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York
Springer
1972
|
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
Band 72 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 354 Seiten |
| ISBN: | 3540059466 |
Staff View
MARC
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| 240 | 1 | 0 | |a Stochasti ceskie differencialnie uravnenija |
| 245 | 1 | 0 | |a Stochastic differential equations |c I. I. Gihman ; A. V. Skorohod ; [Translator: Kenneth Wickwire] |
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer |c 1972 | |
| 300 | |a VIII, 354 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v Band 72 | |
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Record in the Search Index
| _version_ | 1805072017872912384 |
|---|---|
| adam_text |
Table
of
Contents
Introduction
. 1
Part
I. One-dimensional Stochastic Differential Equations of First Order
Chapter
1.
Stochastic Integrals and Differentials
. 7
§ 1.
The Wiener Process
. 7
§ 2.
The Stochastic Integral
. 11
§ 3.
Properties of Stochastic Integrals as Function of the Upper
Limit
. 16
§ 4.
Stochastic Integrals with Random Limits
. 27
Chapter
2.
The Solutions of Stochastic Differential Equations.
. . 33
§ 5.
Stochastic Differential Equations of First Order
. 33
§ 6.
Existence and Uniqueness of the Solutions
. 39
§ 7.
Stochastic Equations which Depend on a Parameter
. 50
§ 8.
Dependence of the Solutions of Stochastic Differential
Equations on the Initial Data
. 59
Chapter
3.
Solutions of Stochastic Differential Equations and Mar¬
kov Diffusion Processes
. 63
§ 9.
Markov Processes. Diffusion Processes
. 63
§ 10.
Diffusion Processes as Solutions of Stochastic Equations
. 67
§11.
Kolmogorov's Equation
. 73
§ 12.
Measures in Function Space Induced by Diffusion Pro¬
cesses
. 80
§13.
Formulas for Transition Density Functions
. 91
§ 14.
Kolmogorov's Equation for the Transition Probability
Density
. 99
§ 15.
Time-homogeneous Solutions of Stochastic Differential
Equations
. 105
Chapter
4.
Asymptotic Behavior of the Solutions of Stochastic
Equations
. 114
§ 16.
Bounded and Unbounded Solutions of Stochastic Equa¬
tions
. 114
§ 17. Theorems
on the Asymptotic Behavior of Solutions
. . . 124
§18.
Ergodic Theorems
. 134
§ 19.
Stability of Solutions
. 145
§20.
Some Other Limit Theorems
. 151
Chapter
5.
Stochastic Differential Equations on a Finite Spatial
Interval
. 159
§ 21.
Boundary Conditions at the Ends of the Interval
. . . .159
§22.
Processes with Absorption at the Boundary
. 165
§23.
Instantaneous Reflection at the Boundary
. 178
§ 24.
Delayed Reflection at the Boundary
. 193
§ 25.
Processes with Jump Reflection at the Boundary
. 205
Part
П.
Systems of Stochastic Differential Equations
Chapter
1.
Vector Stochastic Differential Equations
. 215
§ 1.
Stochastic Line Integrals
. 216
§ 2.
Stochastic Line Integrals as Function of the Upper Limit.
232
§ 3.
Stochastic Differential Equations
. 237
Chapter
2.
Stochastic Differential Equations without After-effect
. 245
§ 4.
Preliminary Remarks
. 245
§ 5.
Some Special Types of Stochastic Integrals
. 247
§ 6.
The Generalized
Ito
Formula for Stochastic Differentials
263
§ 7.
Stochastic Differential Equations without After-effect
. . 273
§ 8.
Stochastic Differential Equations Depending on a Para¬
meter. Diff erentiability w.
r. t
the Initial Data
. 275
§ 9.
Solutions of Stochastic Differential Equations as Markov
Processes
. 288
§ 10.
The Distribution of Functional of the Solutions of Stocha¬
stic Differential Equations
. 300
§11.
Some Problems Connected with Homogeneous Stochastic
Differential Equations
. 304
Chapter
3.
Asymptotic Behavior of the Solutions of Stochastic Dif¬
ferential Equations
.310
§ 12.
Stability of Solutions
.310
§ 13.
Boundedness of the Solutions of Stochastic Differential
Equations
.330
§ 14.
Limit Theorems for Stochastic Differential Equations
. .333
Bibliography
.348
Index
.351 |
| any_adam_object | 1 |
| author | Gichman, Iosif I. 1918-1985 Skorochod, Anatolij V. 1930-2011 |
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| building | Verbundindex |
| bvnumber | BV003012959 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)264144787 (DE-599)BVBBV003012959 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003012959 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T04:47:02Z |
| institution | BVB |
| isbn | 3540059466 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001886196 |
| oclc_num | 264144787 |
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| physical | VIII, 354 Seiten |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Gichman, Iosif I. 1918-1985 (DE-588)128935979 aut Stochasti ceskie differencialnie uravnenija Stochastic differential equations I. I. Gihman ; A. V. Skorohod ; [Translator: Kenneth Wickwire] Berlin ; Heidelberg ; New York Springer 1972 VIII, 354 Seiten txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete Band 72 Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Skorochod, Anatolij V. 1930-2011 (DE-588)128936037 aut Ergebnisse der Mathematik und ihrer Grenzgebiete Band 72 (DE-604)BV005871160 72 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001886196&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gichman, Iosif I. 1918-1985 Skorochod, Anatolij V. 1930-2011 Stochastic differential equations Ergebnisse der Mathematik und ihrer Grenzgebiete Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4057621-8 |
| title | Stochastic differential equations |
| title_alt | Stochasti ceskie differencialnie uravnenija |
| title_auth | Stochastic differential equations |
| title_exact_search | Stochastic differential equations |
| title_full | Stochastic differential equations I. I. Gihman ; A. V. Skorohod ; [Translator: Kenneth Wickwire] |
| title_fullStr | Stochastic differential equations I. I. Gihman ; A. V. Skorohod ; [Translator: Kenneth Wickwire] |
| title_full_unstemmed | Stochastic differential equations I. I. Gihman ; A. V. Skorohod ; [Translator: Kenneth Wickwire] |
| title_short | Stochastic differential equations |
| title_sort | stochastic differential equations |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Stochastische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001886196&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005871160 |
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