Random integral equations with applications to stochastic systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1971
|
| Schriftenreihe: | Lecture notes in mathematics
233 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 166 - 174 |
| Beschreibung: | VII, 174 S. |
Internformat
MARC
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| 100 | 1 | |a Tsokos, Chris P. |d 1937- |e Verfasser |0 (DE-588)1064637736 |4 aut | |
| 245 | 1 | 0 | |a Random integral equations with applications to stochastic systems |c Chris P. Tsokos ; W. J. Padgett |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1971 | |
| 300 | |a VII, 174 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 233 | |
| 500 | |a Literaturverz. S. 166 - 174 | ||
| 700 | 1 | |a Padgett, W. J. |e Verfasser |4 aut | |
| 830 | 0 | |a Lecture notes in mathematics |v 233 |w (DE-604)BV000676446 |9 233 | |
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Datensatz im Suchindex
| _version_ | 1804117284630822912 |
|---|---|
| adam_text | TABLE OF CONTENTS
GENERAL INTRODUCTION 1
I_. PRELIMINARIES 8
1.0 INTRODUCTION 8
1.1 BASIC MATHEMATICAL CONCEPTS 8
1.2 THE STOCHASTIC INTEGRAL EQUATIONS 15
1.3 STOCHASTIC DIFFERENTIAL SYSTEMS 25
II. A RANDOM INTEGRAL EQUATION OF THE VOLTERRA TYPE 27
2.0 INTRODUCTION 27
2.1 SOME PRELIMINARY LEMMAS 28
2.2 EXISTENCE AND UNIQUENESS OF A RANDOM SOLUTION OF
(2.0.1) 30
2.3 SOME SPECIAL CASES 34
2.4 ASYMPTOTIC BEHAVIOR OF THE RANDOM SOLUTION 41
2.5 APPLICATION TO THE POINCARE -LYAPUNOV STABILITY
THEOREM 43
III.APPROXIMATE SOLUTIONS OF THE RANDOM VOLTERRA INTEGRAL
EQUATION 48
3.0 INTRODUCTION 48
3.1 THE METHOD OF SUCCESSIVE APPROXIMATIONS 49
3.1.1 Almost Sure Convergence of Successive
Approximations 51
3.1.2 Rate of Convergence and Mean Square Error of
Approximation 56
VI
3.1.3 Combined Error of Approximation and
Numerical Integration 59
3.2 THE METHOD OF STOCHASTIC APPROXIMATION 66
3.2.1 A Stochastic Approximation Procedure 66
3.2.2 Solution of the Random Volterra Equation
by Stochastic Approximation 68
IV. A STOCHASTIC INTEGRAL EQUATION OF THE FREDHOLM TYPE WITH
APPLICATION TO SYSTEMS THEORY. 76
4.0 INTRODUCTION 76
4.1 EXISTENCE AND UNIQUENESS OF A RANDOM SOLUTION .... 77
4.2 SOME SPECIAL CASES 92
4.3 STOCHASTIC ASYMPTOTIC STABILITY OF THE RANDOM
SOLUTION 96
4.4 AN APPLICATION IN STOCHASTIC CONTROL SYSTEMS 99
V. RANDOM DISCRETE FREDhOLM AND VOLTERRA EQUATIONS. 106
5.0 INTRODUCTION 106
5.1 EXISTENCE AND UNIQUENESS OF A RANDOM SOLUTION . . . .107
5.2 SPECIAL CASES OF THEOREM 5.1.3 112
5.3 STOCHASTIC STABILITY OF THE RANDOM SOLUTION 116
5.4 APPLICATION TO STOCHASTIC SYSTEMS 120
VI¦ THE STOChASTIC DIFFERENTIAL SYSTEMS
x(t;w) = A(o))x(t;aj) + b (w) j (a (t;u) )
WITH
a(t;u) = c(t;u ), x(t;u )
AND
x(t;a ) = A(as)x(t;u)) + b(u) j (a (t;w))
WITH
a(t;w) = f(t;u) +/Q c(t-T;to) ,x(x;u) dT 130
VII
6.0 INTRODUCTION 130
6.1 REDUCTION OF THE STOCHASTIC DIFFERENTIAL SYSTEMS. . .132
6.2 STOCHASTIC ABSOLUTE STABILITY OF THE SYSTEMS 134
VII.THE STOCHASTIC DIFFERENTIAL SYSTEMS
x(t;io) = A(u)x(t;a)) + /|jb (t-n ; o) j) (a (n ;to) )dn
WITH
a(t;co) = f(t;w) + /q c (t-n ;co) , x(n;w) dn
AND
x(t;u ) = A(w)x(t;to) + /gb (t-T ;to) | (a (x ;ai) ) dx
+ /Qc(t-T;w)a(T;u)dT
WITH
a(t;ai) = f(t;w) + /^ d (t-x ;w) , x(x;(o) dT 144
7.0 INTRODUCTION 144
7.1 REDUCTION OF THE STOCHASTIC DIFFERENTIAL SYSTEMS. . .145
7.2 STOCHASTIC ABSOLUTE STABILITY OF THE SYSTEMS 149
VIII.THE STOCHASTIC DIFFERENTIAL SYSTEMS WITH LAG TIME
x(t;w) = A(a))x(t;w) + B (w) x(t-x; u) + b (u) J (a (t; w) )
WITH
a(t;w) = f(t;w) + /Q c(t-s;to) , x(s;to) ds
AND
x(t;w) = A(oo) x(t;u) + B(w)x (t-x; w)
+ /Qn(t-u;uj) (j (a(u;w) )du + b (to) j)(a(t; w) )
WITH
a(t;a ) = f(t;«) + /q c(u;u), x(t-u;w) du 156
8.0 INTRODUCTION 156
8.1 REDUCTION OF THE STOChASTIC DIFFERENTIAL SYSTEMS. . .158
8.2 STOCbASTIC ABSOLUTE STABILITY OF THE SYSTEMS 161
REFERENCES 166
|
| any_adam_object | 1 |
| author | Tsokos, Chris P. 1937- Padgett, W. J. |
| author_GND | (DE-588)1064637736 |
| author_facet | Tsokos, Chris P. 1937- Padgett, W. J. |
| author_role | aut aut |
| author_sort | Tsokos, Chris P. 1937- |
| author_variant | c p t cp cpt w j p wj wjp |
| building | Verbundindex |
| bvnumber | BV002995231 |
| ctrlnum | (OCoLC)889083512 (DE-599)BVBBV002995231 |
| dewey-full | 510/.8 515/.45 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510/.8 515/.45 |
| dewey-search | 510/.8 515/.45 |
| dewey-sort | 3510 18 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002995231 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:51:58Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001875113 |
| oclc_num | 889083512 |
| open_access_boolean | |
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| physical | VII, 174 S. |
| psigel | TUB-www HUB-ZB011201202 |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Tsokos, Chris P. 1937- Verfasser (DE-588)1064637736 aut Random integral equations with applications to stochastic systems Chris P. Tsokos ; W. J. Padgett Berlin [u.a.] Springer 1971 VII, 174 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 233 Literaturverz. S. 166 - 174 Padgett, W. J. Verfasser aut Lecture notes in mathematics 233 (DE-604)BV000676446 233 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001875113&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tsokos, Chris P. 1937- Padgett, W. J. Random integral equations with applications to stochastic systems Lecture notes in mathematics |
| title | Random integral equations with applications to stochastic systems |
| title_auth | Random integral equations with applications to stochastic systems |
| title_exact_search | Random integral equations with applications to stochastic systems |
| title_full | Random integral equations with applications to stochastic systems Chris P. Tsokos ; W. J. Padgett |
| title_fullStr | Random integral equations with applications to stochastic systems Chris P. Tsokos ; W. J. Padgett |
| title_full_unstemmed | Random integral equations with applications to stochastic systems Chris P. Tsokos ; W. J. Padgett |
| title_short | Random integral equations with applications to stochastic systems |
| title_sort | random integral equations with applications to stochastic systems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001875113&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT tsokoschrisp randomintegralequationswithapplicationstostochasticsystems AT padgettwj randomintegralequationswithapplicationstostochasticsystems |