Verfügbarkeit: Two-scale stochastic systems | Technische Universität München

Two-scale stochastic systems: asymptotic analysis and control

Gespeichert in:

Bibliographische Detailangaben
Beteiligte Personen:	Kabanov, Jurij M. 1948- (VerfasserIn), Pergamenščikov, Sergej M. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 2003
Schriftenreihe:	Applications of mathematics 49
Schlagwörter:	Stochastische Differentialgleichung - Singuläre Störung Stochastische Differentialgleichung Singuläre Störung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010049558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Literaturverz. S. 259 - 263
Umfang:	XIV, 266 S. 24 cm
ISBN:	3540653325

Internformat

MARC


LEADER	00000nam a2200000 cb4500
001	BV014862163
003	DE-604
005	20230329
007	t\|
008	021105s2003 gw \|\|\|\| \|\|\|\| 00\|\|\| eng d
016	7		\|a 965264548 \|2 DE-101
020			\|a 3540653325 \|9 3-540-65332-5
035			\|a (OCoLC)248761056
035			\|a (DE-599)BVBBV014862163
040			\|a DE-604 \|b ger \|e rakddb
041	0		\|a eng
044			\|a gw \|c DE
049			\|a DE-91 \|a DE-91G \|a DE-824 \|a DE-83 \|a DE-188
050		0	\|a QA402.37
082	0		\|a 003.76
084			\|a SK 820 \|0 (DE-625)143258: \|2 rvk
084			\|a MAT 606f \|2 stub
084			\|a 93Exx \|2 msc
100	1		\|a Kabanov, Jurij M. \|d 1948- \|e Verfasser \|0 (DE-588)124079199 \|4 aut
245	1	0	\|a Two-scale stochastic systems \|b asymptotic analysis and control \|c Yuri Kabanov ; Sergei Pergamanshchikov
264		1	\|a Berlin [u.a.] \|b Springer \|c 2003
300			\|a XIV, 266 S. \|b 24 cm
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
490	1		\|a Applications of mathematics \|v 49
500			\|a Literaturverz. S. 259 - 263
650		4	\|a Stochastische Differentialgleichung - Singuläre Störung
650	0	7	\|a Stochastische Differentialgleichung \|0 (DE-588)4057621-8 \|2 gnd \|9 rswk-swf
650	0	7	\|a Singuläre Störung \|0 (DE-588)4055100-3 \|2 gnd \|9 rswk-swf
689	0	0	\|a Stochastische Differentialgleichung \|0 (DE-588)4057621-8 \|D s
689	0	1	\|a Singuläre Störung \|0 (DE-588)4055100-3 \|D s
689	0		\|5 DE-604
700	1		\|a Pergamenščikov, Sergej M. \|e Verfasser \|0 (DE-588)120524562 \|4 aut
830		0	\|a Applications of mathematics \|v 49 \|w (DE-604)BV000895226 \|9 49
856	4	2	\|m SWB Datenaustausch \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010049558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
943	1		\|a oai:aleph.bib-bvb.de:BVB01-010049558

Datensatz im Suchindex

DE-BY-TUM_call_number	0001 08.2003 A 82 0102 MAT 606f 2001 A 20010
DE-BY-TUM_katkey	1383706
DE-BY-TUM_location	Mag 01
DE-BY-TUM_media_number	040005133075 040020129480
_version_	1821932890615709698
adam_text	TABLE OF CONTENTS INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX 0 WARM-UP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.1 PROCESSES WITH FAST MARKOV MODULATIONS . . . . . . . . . . . . . . . . . . 1 0.1.1 MODEL FORMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.1.2 ASYMPTOTIC BEHAVIOR OF D ISTRIBUTIONS . . . . . . . . . . . . . . . 2 0.2 THE LI´ ENARD OSCILLATOR UNDER RANDOM FORCE . . . . . . . . . . . . . . . 6 0.3 FILTERING OF NEARLY OBSERVED PROCESSES . . . . . . . . . . . . . . . . . . . . 9 0.4 STOCHASTIC APPROXIMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1 TOOLBOX: MOMENT BOUNDS FOR SOLUTIONS OF STABLE SDES . . . 19 1.1 MOMENT BOUNDS FOR NONLINEAR EQUATIONS . . . . . . . . . . . . . . . . . . 20 1.1.1 KEY LEMMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.1.2 BOUNDS EFFICIENT ON SMALL INTERVALS . . . . . . . . . . . . . . . . . 22 1.1.3 BOUNDS EFFICIENT ON LARGE INTERVALS . . . . . . . . . . . . . . . . . 24 1.2 BOUNDS FOR LINEAR EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.2.1 ASSUMPTION ON THE FUNDAMENTAL MATRIX. . . . . . . . . . . . . 26 1.2.2 DIFFERENTIAL EQUATIONS WITH RANDOM COEFFICIENTS . . . . . 27 1.2.3 THE CONTINUITY THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.2.4 LINEAR SDES WITH UNBOUNDED COEFFICIENTS . . . . . . . . . . . 31 1.3 ON THE GROWTH RATE OF THE MAXIMAL FUNCTION . . . . . . . . . . . . . 34 1.3.1 LAPEYRES INEQUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.3.2 ORNSTEINUHLENBECK PROCESS . . . . . . . . . . . . . . . . . . . . . . . 37 1.3.3 SAMPLE PATH GROWTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1.3.4 FERNIQUES LEMMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2 THE TIKHONOV THEORY FOR SDES . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.1 THE STOCHASTIC TIKHONOV THEOREM . . . . . . . . . . . . . . . . . . . . . . . . 45 2.1.1 SETTING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.1.2 BOUNDARY LAYER BEHAVIOR . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.1.3 LARGE SCALE BEHAVIOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.1.4 CONCLUDING STEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 VI TABLE OF CONTENTS 2.2 THE FIRST-ORDER ASYMPTOTICS FOR FAST VARIABLES . . . . . . . . . . . . 56 2.2.1 BASIC HYPOTHESES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.2.2 THE FIRST-ORDER CORRECTION . . . . . . . . . . . . . . . . . . . . . . . . 57 2.2.3 THE FIRST-ORDER APPROXIMATION OF THE REST POINT . . . . 59 2.2.4 NORMAL APPROXIMATION RESULT . . . . . . . . . . . . . . . . . . . . . 62 2.3 HIGHER-ORDER EXPANSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.3.1 FORMAL EXPANSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.3.2 CONVERGENCE OF THE REMAINDER . . . . . . . . . . . . . . . . . . . . . 65 2.3.3 EXPANSION AROUND THE REST POINT . . . . . . . . . . . . . . . . . . 69 2.4 STOCHASTIC APPROXIMATION: PROOFS . . . . . . . . . . . . . . . . . . . . . . . . 70 2.4.1 ASYMPTOTIC EXPANSION FOR THE OUTPUT SIGNAL . . . . . . . . 70 2.4.2 THE ASYMPTOTIC EXPANSION AT THE ROOT . . . . . . . . . . . . . 78 2.4.3 AVERAGING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.4.4 PROOF OF THEOREM 0.4.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3 LARGE DEVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.1 D EVIATIONS IN THE UNIFORM METRIC . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.1.1 FORMULATION OF THE RESULT . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.1.2 A LOWER EXPONENTIAL BOUND FOR THE NON-EXIT PROBABILITY . . . . . . . . . . . . . . . . . . . . . . . 89 3.1.3 AN UPPER BOUND FOR THE PROBABILITY OF DEVIATION OF A TRAJECTORY FROM THE LEBESGUE SETS OF S T . . . . . . . . 91 3.1.4 PROOF OF THEOREM 3.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.1.5 EXAMPLE: THE ORNSTEINUHLENBECK PROCESS . . . . . . . . . . . 104 3.2 DEVIATIONS IN THE METRIC OF L 2 [0 ,T ] . . . . . . . . . . . . . . . . . . . . . . . 105 4 UNIFORM EXPANSIONS FOR TWO-SCALE SYSTEMS . . . . . . . . . . . . . . . 111 4.1 NO D IFFUSION AT THE FAST VARIABLE . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.1.1 FORMAL CALCULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.1.2 INTEGRABILITY OF COEFFICIENTS . . . . . . . . . . . . . . . . . . . . . . . . 119 4.1.3 THE BOUNDARY LAYER FUNCTION OF ZERO ORDER . . . . . . . . . 120 4.1.4 BOUNDARY LAYER FUNCTIONS OF HIGHER ORDER . . . . . . . . . . 124 4.1.5 PROOF OF THEOREM 4.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.2 EXPANSIONS FOR THE GENERAL MODEL . . . . . . . . . . . . . . . . . . . . . . . . 133 4.2.1 FORMULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.2.2 GROWTH OF COEFFICIENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.2.3 PROOF OF THEOREM 4.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 4.3 LI´ ENARD OSCILLATOR DRIVEN BY A RANDOM FORCE . . . . . . . . . . . . . . 140 TABLE OF CONTENTS VII 5 TWO-SCALE OPTIMAL CONTROL PROBLEMS . . . . . . . . . . . . . . . . . . . . . 145 5.1 SEMILINEAR CONTROLLED SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.1.1 THE MODEL AND MAIN RESULT . . . . . . . . . . . . . . . . . . . . . . . 146 5.1.2 PROOF OF PROPOSITION 5.1.2 . . . . . . . . . . . . . . . . . . . . . . . . . 148 5.1.3 PROOF OF PROPOSITION 5.1.3 . . . . . . . . . . . . . . . . . . . . . . . . . 155 5.1.4 PROOF OF THEOREM 5.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 5.2 STRUCTURE OF THE ATTAINABILITY SETS . . . . . . . . . . . . . . . . . . . . . . . . 158 5.2.1 WEAK AND STRONG SOLUTIONS OF SD ES . . . . . . . . . . . . . . . . 158 5.2.2 CLOSED LOOP CONTROLS VERSUS OPEN LOOP . . . . . . . . . . . . 160 5.2.3 TUBES* AND ATTAINABILITY SETS FOR FEEDBACK CONTROLS . 164 5.2.4 EXTREME POINTS OF THE SET OF ATTAINABLE DENSITIES . . . . 167 5.2.5 ON THE EXISTENCE OF OPTIMAL CONTROL . . . . . . . . . . . . . . . 169 5.2.6 COMPARISON OF ATTAINABILITY SETS . . . . . . . . . . . . . . . . . . . 171 5.3 CONVERGENCE OF THE ATTAINABILITY SETS, I . . . . . . . . . . . . . . . . . . . 175 5.3.1 THE D ONTCHEV*VELIOV THEOREM . . . . . . . . . . . . . . . . . . . . . 175 5.3.2 THE FIRST STOCHASTIC GENERALIZATION . . . . . . . . . . . . . . . . . 176 5.4 CONVERGENCE OF THE ATTAINABILITY SETS, II . . . . . . . . . . . . . . . . . . 180 5.4.1 FORMULATION OF THE RESULT . . . . . . . . . . . . . . . . . . . . . . . . . 180 5.4.2 THE FAST VARIABLE MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . 182 5.4.3 GENERAL CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 5.4.4 PROOF OF THEOREM 5.4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 6 APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 6.1 APPLICATIONS TO PD ES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 6.2 FAST MARKOV MODULATIONS REVISITED . . . . . . . . . . . . . . . . . . . . . . . 199 6.2.1 MAIN RESULT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 6.2.2 PRELIMINARIES FROM WEAK CONVERGENCE . . . . . . . . . . . . . . . 200 6.2.3 PROOF OF THEOREM 6.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 6.2.4 CALCULATIONS AND ESTIMATES . . . . . . . . . . . . . . . . . . . . . . . . 203 6.2.5 COX PROCESSES WITH FAST MARKOV MODULATIONS . . . . . . . . 206 6.3 ACCURACY OF APPROXIMATE FILTERS . . . . . . . . . . . . . . . . . . . . . . . . . 207 6.4 SIGNAL ESTIMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 6.5 LINEAR REGULATOR WITH INFINITE HORIZON . . . . . . . . . . . . . . . . . . . . 213 6.5.1 SENSITIVE PROBABILISTIC CRITERIA . . . . . . . . . . . . . . . . . . . . . 213 6.5.2 LINEAR-QUADRATIC REGULATOR . . . . . . . . . . . . . . . . . . . . . . . . 214 6.5.3 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 6.5.4 PROOF OF THEOREM 6.5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.5.5 EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 VIII TABLE OF CONTENTS APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 A.1 BASIC FACTS ABOUT SD ES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 A.1.1 EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS FOR SD ES WITH RANDOM COEFFICIENTS . . . . . . . . . . . . . . . . . 223 A.1.2 EXISTENCE AND UNIQUENESS WITH A LYAPUNOV FUNCTION . 224 A.1.3 MOMENT BOUNDS FOR LINEAR SDES . . . . . . . . . . . . . . . . . . . 225 A.1.4 THE NOVIKOV CONDITION . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 A.2 EXPONENTIAL BOUNDS FOR FUNDAMENTAL MATRICES . . . . . . . . . . . . . 227 A.2.1 UNIFORM BOUND IN THE TIME-HOMOGENEOUS CASE . . . . . . 227 A.2.2 NONHOMOGENEOUS CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 A.2.3 MODELS WITH SINGULAR PERTURBATIONS . . . . . . . . . . . . . . . . . 230 A.3 TOTAL VARIATION DISTANCE AND HELLINGER PROCESSES . . . . . . . . . . . 234 A.3.1 TOTAL VARIATION DISTANCE AND HELLINGER INTEGRALS . . . . . . 234 A.3.2 THE HELLINGER PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 A.3.3 EXAMPLE: D IFFUSION-TYPE PROCESSES . . . . . . . . . . . . . . . . . 238 A.4 HAUSDORFF METRIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 A.5 MEASURABLE SELECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 A.5.1 AUMANN THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 A.5.2 FILIPPOV IMPLICIT FUNCTION LEMMA . . . . . . . . . . . . . . . . . . 241 A.5.3 MEASURABLE VERSION OF THE CARATH´ EODORY THEOREM . . . . 241 A.6 COMPACT SETS IN P ( X ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 A.6.1 NOTATIONS AND PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . 243 A.6.2 INTEGRATION OF STOCHASTIC KERNELS . . . . . . . . . . . . . . . . . . . 245 A.6.3 D ISTRIBUTIONS OF INTEGRALS . . . . . . . . . . . . . . . . . . . . . . . . . . 246 A.6.4 COMPACTNESS OF THE LIMIT OF ATTAINABILITY SETS . . . . . . . 248 A.6.5 SUPPORTS OF CONDITIONAL DISTRIBUTIONS . . . . . . . . . . . . . . . 250 A.7 THE KOML´ OS THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 HISTORICAL NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
any_adam_object	1
author	Kabanov, Jurij M. 1948- Pergamenščikov, Sergej M.
author_GND	(DE-588)124079199 (DE-588)120524562
author_facet	Kabanov, Jurij M. 1948- Pergamenščikov, Sergej M.
author_role	aut aut
author_sort	Kabanov, Jurij M. 1948-
author_variant	j m k jm jmk s m p sm smp
building	Verbundindex
bvnumber	BV014862163
callnumber-first	Q - Science
callnumber-label	QA402
callnumber-raw	QA402.37
callnumber-search	QA402.37
callnumber-sort	QA 3402.37
callnumber-subject	QA - Mathematics
classification_rvk	SK 820
classification_tum	MAT 606f
ctrlnum	(OCoLC)248761056 (DE-599)BVBBV014862163
dewey-full	003.76
dewey-hundreds	000 - Computer science, information, general works
dewey-ones	003 - Systems
dewey-raw	003.76
dewey-search	003.76
dewey-sort	13.76
dewey-tens	000 - Computer science, information, general works
discipline	Informatik Mathematik
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01890nam a2200469 cb4500</leader><controlfield tag="001">BV014862163</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230329 </controlfield><controlfield tag="007">t\|</controlfield><controlfield tag="008">021105s2003 gw \|\|\|\| \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">965264548</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540653325</subfield><subfield code="9">3-540-65332-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)248761056</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014862163</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="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA402.37</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">003.76</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 606f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">93Exx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kabanov, Jurij M.</subfield><subfield code="d">1948-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)124079199</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Two-scale stochastic systems</subfield><subfield code="b">asymptotic analysis and control</subfield><subfield code="c">Yuri Kabanov ; Sergei Pergamanshchikov</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 266 S.</subfield><subfield code="b">24 cm</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">Applications of mathematics</subfield><subfield code="v">49</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 259 - 263</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastische Differentialgleichung - Singuläre Störung</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastische Differentialgleichung</subfield><subfield code="0">(DE-588)4057621-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Singuläre Störung</subfield><subfield code="0">(DE-588)4055100-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Stochastische Differentialgleichung</subfield><subfield code="0">(DE-588)4057621-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Singuläre Störung</subfield><subfield code="0">(DE-588)4055100-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pergamenščikov, Sergej M.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)120524562</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Applications of mathematics</subfield><subfield code="v">49</subfield><subfield code="w">(DE-604)BV000895226</subfield><subfield code="9">49</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">SWB 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=010049558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-010049558</subfield></datafield></record></collection>
id	DE-604.BV014862163
illustrated	Not Illustrated
indexdate	2024-12-20T11:08:59Z
institution	BVB
isbn	3540653325
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-010049558
oclc_num	248761056
open_access_boolean
owner	DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-824 DE-83 DE-188
owner_facet	DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-824 DE-83 DE-188
physical	XIV, 266 S. 24 cm
publishDate	2003
publishDateSearch	2003
publishDateSort	2003
publisher	Springer
record_format	marc
series	Applications of mathematics
series2	Applications of mathematics
spellingShingle	Kabanov, Jurij M. 1948- Pergamenščikov, Sergej M. Two-scale stochastic systems asymptotic analysis and control Applications of mathematics Stochastische Differentialgleichung - Singuläre Störung Stochastische Differentialgleichung (DE-588)4057621-8 gnd Singuläre Störung (DE-588)4055100-3 gnd
subject_GND	(DE-588)4057621-8 (DE-588)4055100-3
title	Two-scale stochastic systems asymptotic analysis and control
title_auth	Two-scale stochastic systems asymptotic analysis and control
title_exact_search	Two-scale stochastic systems asymptotic analysis and control
title_full	Two-scale stochastic systems asymptotic analysis and control Yuri Kabanov ; Sergei Pergamanshchikov
title_fullStr	Two-scale stochastic systems asymptotic analysis and control Yuri Kabanov ; Sergei Pergamanshchikov
title_full_unstemmed	Two-scale stochastic systems asymptotic analysis and control Yuri Kabanov ; Sergei Pergamanshchikov
title_short	Two-scale stochastic systems
title_sort	two scale stochastic systems asymptotic analysis and control
title_sub	asymptotic analysis and control
topic	Stochastische Differentialgleichung - Singuläre Störung Stochastische Differentialgleichung (DE-588)4057621-8 gnd Singuläre Störung (DE-588)4055100-3 gnd
topic_facet	Stochastische Differentialgleichung - Singuläre Störung Stochastische Differentialgleichung Singuläre Störung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010049558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000895226
work_keys_str_mv	AT kabanovjurijm twoscalestochasticsystemsasymptoticanalysisandcontrol AT pergamenscikovsergejm twoscalestochasticsystemsasymptoticanalysisandcontrol

Verfügbarkeit

Bestellen (Login erforderlich)

Inhaltsverzeichnis
Paper/Kapitel scannen lassen

Bibliotheksmagazin

Bestandsangaben von Bibliotheksmagazin
Signatur:	0001 08.2003 A 82 Lageplan
Exemplar 1	Ausleihbar Ausgeliehen – Rückgabe bis: 31.12.9999

Teilbibliothek Mathematik & Informatik

Bestandsangaben von Teilbibliothek Mathematik & Informatik
Signatur:	0102 MAT 606f 2001 A 20010 Lageplan
Exemplar 1	Ausleihbar Am Standort