Verfügbarkeit: Random integral equations with applications to stochastic systems

Random integral equations with applications to stochastic systems:

Gespeichert in:

Bibliographische Detailangaben
Beteiligte Personen:	Tsokos, Chris P. 1937- (VerfasserIn), Padgett, W. J. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 1971
Schriftenreihe:	Lecture notes in mathematics 233
Links:	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
Beschreibung:	Literaturverz. S. 166 - 174
Umfang:	VII, 174 S.

Internformat

MARC


LEADER	00000nam a2200000 cb4500
001	BV002995231
003	DE-604
005	20121205
007	t\|
008	900725s1971 xx \|\|\|\| 00\|\|\| eng d
035			\|a (OCoLC)889083512
035			\|a (DE-599)BVBBV002995231
040			\|a DE-604 \|b ger \|e rakddb
041	0		\|a eng
049			\|a DE-12 \|a DE-384 \|a DE-91G \|a DE-355 \|a DE-20 \|a DE-824 \|a DE-29T \|a DE-19 \|a DE-706 \|a DE-83 \|a DE-188 \|a DE-11 \|a DE-210
082	0		\|a 510/.8
082	0		\|a 515/.45
084			\|a 93E03 \|2 msc
084			\|a 60H20 \|2 msc
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
856	4	2	\|m HBZ Datenaustausch \|q application/pdf \|u 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 \|3 Inhaltsverzeichnis
940	1		\|q TUB-www
940	1		\|q HUB-ZB011201202
943	1		\|a oai:aleph.bib-bvb.de:BVB01-001875113

Datensatz im Suchindex

DE-BY-TUM_call_number	0102 MAT 001z 2001 B 999-233
DE-BY-TUM_katkey	487493
DE-BY-TUM_location	01
DE-BY-TUM_media_number	040020160229
_version_	1821938845479862272
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
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01436nam a2200373 cb4500</leader><controlfield tag="001">BV002995231</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20121205 </controlfield><controlfield tag="007">t\|</controlfield><controlfield tag="008">900725s1971 xx \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)889083512</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002995231</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-210</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510/.8</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.45</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">93E03</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60H20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Tsokos, Chris P.</subfield><subfield code="d">1937-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1064637736</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Random integral equations with applications to stochastic systems</subfield><subfield code="c">Chris P. Tsokos ; W. J. Padgett</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1971</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VII, 174 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">233</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 166 - 174</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Padgett, W. J.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">233</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">233</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">TUB-www</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">HUB-ZB011201202</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001875113</subfield></datafield></record></collection>
id	DE-604.BV002995231
illustrated	Not Illustrated
indexdate	2024-12-20T07:57:08Z
institution	BVB
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-001875113
oclc_num	889083512
open_access_boolean
owner	DE-12 DE-384 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-188 DE-11 DE-210
owner_facet	DE-12 DE-384 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-188 DE-11 DE-210
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
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

Verfügbarkeit

Bestellen (Login erforderlich)

Inhaltsverzeichnis
Paper/Kapitel scannen lassen

Teilbibliothek Mathematik & Informatik

Bestandsangaben von Teilbibliothek Mathematik & Informatik
Signatur:	0102 MAT 001z 2001 B 999-233 Lageplan
Exemplar 1	Ausleihbar Am Standort