Stochastic integration with jumps:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2002
|
| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
89 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIII, 501 S. Illustrationen |
| ISBN: | 0521811295 9780521811293 9780521142144 |
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Record in the Search Index
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| adam_text | ENCYCLOPEDIA OF MATHEMATICS AND ITS APPUCATIONS STOCHASTIC INTEGRATION
WITH JUMPS KLAUS BICHTELER UNIVERSITY OF TEXAS AT AUSTIN CAMBRIDGE
UNIVERSITY PRESS CONTENTS PREFACE XI CHAPTER 1 INTRODUCTION 1 1.1
MOTIVATION: STOCHASTIC DIFFERENTIAL EQUATIONS 1 THE OBSTACLE 4, ITO S
WAY OUT OF THE QUANDARY 5, SUMMARY: THE TASK AHEAD 6 1.2 WIENER PROCESS
9 EXISTENCE OF WIENER PROCESS 11, UNIQUENESS OF WIENER MEASURE 14, NON-
DIFFERENTIABILITY OF THE WIENER PATH 17, SUPPLEMENTS AND ADDITIONAL
EXERCISES 18 1.3 THE GENERAL MODEL 20 FILTRATIONS ON MEASURABLE SPACES
21, THE BASE SPACE 22, PROCESSES 23, STOP- PING TIMES AND STOCHASTIC
INTERVALS 27, SOME EXAMPLES OF STOPPING TIMES 29, PROBABILITIES 32, THE
SIZES OF RANDOM VARIABLES 33, TWO NOTIONS OF EQUALITY FOR PROCESSES 34,
THE NATURAL CONDITIONS 36 CHAPTER 2 INTEGRATORS AND MARTINGALES 43 STEP
FUNCTIONS ARID LEBESGUE*STIELTJES INTEGRATORS ON THE LINE 43 2.1 THE
ELEMENTARY STOCHASTIC INTEGRAL 46 ELEMENTARY STOCHASTIC INTEGRANDS 46,
THE ELEMENTARY STOCHASTIC INTEGRAL 47, THE ELEMENTARY INTEGRAL AND
STOPPING TIMES 47, L P -INTEGRATORS 49, LOCAL PROPERTIES 51 2.2 THE
SEMIVARIATIONS 53 THE SIZE OF AN INTEGRATOR 54, VECTORS OF INTEGRATORS
56, THE NATURAL CONDITIONS 56 2.3 PATH REGULARITY OF INTEGRATORS . .-
58 RIGHT-CONTINUITY AND LEFT LIMITS 58, BOUNDEDNESS OF THE PATHS 61,
REDEFINITION OF INTEGRATORS 62, THE MAXIMAL INEQUALITY 63, LAW AND
CANONICAL REPRESENTATION 64 2.4 PROCESSES OF FINITE VARIATION 67
DECOMPOSITION INTO CONTINUOUS AND JUMP PARTS 69, THE CHANGE-OF-VARIABLE
FORMULA 70 2.5 MARTINGALES 71 SUBMARTINGALES AND SUPERMARTINGALES 73,
REGULARITY OF THE PATHS: RIGHT- CONTINUITY AND LEFT. LIMITS 74,
BOUNDEDNESS OF THE PATHS 76, DOOB S OPTIONAL STOPPING THEOREM 77,
MARTINGALES ARE INTEGRATORS 78, MARTINGALES IN L P 80 CHAPTER 3
EXTENSION OF THE INTEGRAL :,.... 87 DANIELL S EXTENSION PROCEDURE ON THE
LINE 87 3.1 THE DANIELL MEAN . 88 A TEMPORARY ASSUMPTION 89, PROPERTIES
OF THE DANIELL MEAN 90 3.2 THE INTEGRATION THEORY OF A MEAN 94
NEGLIGIBLE FUNCTIONS AND SETS 95, PROCESSES FINITE FOR THE MEAN AND
DEFINED ALMOST EVERYWHERE 97, INTEGRABLE PROCESSES AND THE STOCHASTIC
INTEGRAL 99, PERMANENCE PROPERTIES OF INTEGRABLE FUNCTIONS 101,
PERMANENCE UNDER ALGEBRAIC AND ORDER OPERATIONS 101, PERMANENCE UNDER
POINTWISE LIMITS OF SEQUENCES 102, INTEGRABLE SETS 104 VU VIII CONTENTS
3.3 COUNTABLE ADDITIVITY IN P-ME&N 106 THE INTEGRATION THEORY OF VECTORS
OF INTEGRATORS 109 3.4 MEASURABILITY 110 PERMANENCE UNDER LIMITS OF
SEQUENCES 111, PERMANENCE UNDER ALGEBRAIC AND ORDER OPERATIONS 112, THE
INTEGRABILITY CRITERION 113, MEASURABLE SETS 114 3.5 PREDICTABLE AND
PREVISIBLE PROCESSES 115 PREDICTABLE PROCESSES 115, PREVISIBLE PROCESSES
118, PREDICTABLE STOPPING TIMES 118, ACCESSIBLE STOPPING TIMES 122 3.6
SPECIAL PROPERTIES OF DANIELL S MEAN 123 MAXIMALITY 123, CONTINUITY
ALONG INCREASING SEQUENCES 124, PREDICTABLE ENVELOPES 125, REGULARITY
128, STABILITY UNDER CHANGE OF MEASURE 129 3.7 THE INDEFINITE INTEGRAL
130 THE INDEFINITE INTEGRAL 132, INTEGRATION THEORY OF THE INDEFINITE
INTEGRAL 135, A GENERAL INTEGRABILITY CRITERION 137, APPROXIMATION OF
THE INTEGRAL VIA PARTI- TIONS 138, PATHWISE COMPUTATION OF THE
INDEFINITE INTEGRAL 140, INTEGRATORS OF FINITE VARIATION 144 3.8
FUNCTIONS OF INTEGRATORS 145 SQUARE BRACKET AND SQUARE FUNCTION OF AN
INTEGRATOR 148, THE SQUARE BRACKET OF TWO INTEGRATORS 150, THE SQUARE
BRACKET OF AN INDEFINITE INTEGRAL 153, APPLICATION: THE JUMP OF AN
INDEFINITE INTEGRAL 155 3.9 ITO S FORMULA 157 THE DOLEANS-DADE
EXPONENTIAL 159, ADDITIONAL EXERCISES 161, GIRSANOV THEO- REMS 162, THE
STRATONOVICH INTEGRAL 168 3.10 RANDOM MEASURES 171 CT-ADDITIVITY 174,
LAW AND CANONICAL REPRESENTATION 175, EXAMPLE: WIENER RANDOM MEASURE
177, EXAMPLE: THE JUMP MEASURE OF AN INTEGRATOR 180, STRICT RANDOM
MEASURES AND POINT PROCESSES 183, EXAMPLE: POISSON POINT PROCESSES 184,
THE GIRSANOV THEOREM FOR POISSON POINT PROCESSES 185 CHAPTER 4 CONTROL
OF INTEGRAL AND INTEGRATOR 187 4.1 . CHANGE OF MEASURE * FACTORIZATION
187 A SIMPLE CASE 187, THE MAIN FACTORIZATION THEOREM 191, PROOF FOR P
0 195, PROOF FOR P = 0 205 4.2 MARTINGALE INEQUALITIES 209 FEFFERMAN S
INEQUALITY 209, THE BURKHOLDER-DAVIS-GUNDY INEQUALITIES 213, THE HARDY
MEAN 216, MARTINGALE REPRESENTATION ON WIENER SPACE 218, ADDITIONAL
EXERCISES 219 4.3 THE DOOB-MEYER DECOMPOSITION 221 DOLEANS-DADE MEASURES
AND PROCESSES 222, PROOF OF THEOREM 4.3.1: NECESSITY, UNIQUENESS, AND
EXISTENCE 225, PROOF OF THEOREM 4.3.1: THE INEQUALITIES 227, THE,
PREVISIBLE SQUARE FUNCTION 228, THE DOOB*MEYER DECOMPOSITION OF A RANDOM
MEASURE 231 4.4 SEMIMARTINGALES 232 INTEGRATORS ARE SEMIMARTINGALES 233,
VARIOUS DECOMPOSITIONS OF AN INTEGRATOR 234 4.5 .. PREVISIBLE CONTROL OF
INTEGRATORS 238 CONTROLLING A SINGLE INTEGRATOR 239, PREVISIBLE CONTROL
OF VECTORS OF INTEGRATORS 246, PREVISIBLE CONTROL OF RANDOM MEASURES 251
4.6 LEVY PROCESSES 253 THE LEVY-KHINTCHINE FORMULA 257, THE MARTINGALE
REPRESENTATION THEOREM 261, CANONICAL COMPONENTS OF A LEVY PROCESS 265,
CONSTRUCTION OF LEVY PROCESSES 267, FELLER SEMIGROUP AND GENERATOR 268
CONTENTS IX CHAPTER 5 STOCHASTIC DIFFERENTIAL EQUATIONS 271 5.1
INTRODUCTION 271 FIRST ASSUMPTIONS ON THE DATA AND DEFINITION OF
SOLUTION 272, EXAMPLE: THE ORDINARY DIFFERENTIAL EQUATION (ODE) 273,
ODE: FLOWS AND ACTIONS 278, ODE: APPROXIMATION 280 5.2 J EXISTENCE AND
UNIQUENESS OF THE SOLUTION 282 THE PICARD NORMS 283, LIPSCHITZ
CONDITIONS 285, EXISTENCE AND UNIQUENESS OF THE SOLUTION 289, STABILITY
293, DIFFERENTIAL EQUATIONS DRIVEN BY RANDOM MEASURES 296, THE CLASSICAL
SDE 297 5.3 STABILITY: DIFFERENTIABILITY IN PARAMETERS 298 THE
DERIVATIVE OF THE SOLUTION 301, PATHWISE DIFFERENTIABILITY 303, HIGHER
ORDER DERIVATIVES 305 5.4 PATHWISE COMPUTATION OF THE SOLUTION 310 THE
CASE OF MARKOVIAN COUPLING COEFFICIENTS 311, THE CASE OF ENDOGENOUS COU-
PLING COEFFICIENTS 314, THE UNIVERSAL SOLUTION 316, A NON-ADAPTIVE
SCHEME 317, THE STRATONOVICH EQUATION 320, HIGHER ORDER APPROXIMATION:
OBSTRUCTIONS 321, HIGHER ORDER APPROXIMATION: RESULTS 326 5.5 WEAK
SOLUTIONS 330 THE SIZE OF THE SOLUTION 332, EXISTENCE OF WEAK SOLUTIONS
333, UNIQUENESS 337 5.6 STOCHASTIC FLOWS 343 STOCHASTIC FLOWS WITH A
CONTINUOUS DRIVER 343, DRIVERS WITH SMALL JUMPS 346, MARKOVIAN
STOCHASTIC FLOWS 347, MARKOVIAN STOCHASTIC FLOWS DRIVEN BY A LEVY
PROCESS 349 5.7 SEMIGROUPS, MARKOV PROCESSES, AND PDE 351 STOCHASTIC
REPRESENTATION OF FELLER SEMIGROUPS 351 APPENDIX A COMPLEMENTS TO
TOPOLOGY AND MEASURE THEORY ... . 363 A.I NOTATIONS AND CONVENTIONS _.
363 A.2 TOPOLOGICAL MISCELLANEA 366 THE THEOREM OF STONE-WEIERSTRAFI
366, TOPOLOGIES, FILTERS ;-UNIFORMITIES 373, SEMI- CONTINUITY 376,
SEPARABLE METRIC SPACES 377, TOPOLOGICAL VECTOR SPACES 379, THE MINIMAX
THEOREM, LEMMAS OF GRONWALL AND KOLMOGOROFF 382, DIFFERENTIATION 388 A.3
MEASURE AND INTEGRATION 391 CR-ALGEBRAS 391, SEQUENTIAL CLOSURE 391,
MEASURES AND INTEGRALS 394, ORDER- CONTINUOUS AND TIGHT ELEMENTARY
INTEGRALS 398, PROJECTIVE SYSTEMS OF MEA- SURES 401, PRODUCTS OF
ELEMENTARY INTEGRALS 402, INFINITE PRODUCTS OF ELEMENTARY INTEGRALS 404,
IMAGES, LAW, AND DISTRIBUTION 405, THE VECTOR LATTICE OF ALL MEA- SURES
406, CONDITIONAL EXPECTATION 407, NUMERICAL AND CHARACTERISTIC FUNCTIONS
409, CONVOLUTION 413, LIFTINGS, DISINTEGRATION OF MEA- SURES 414,
GAUSSIAN AND POISSON RANDOM VARIABLES 419 A.4 WEAK CONVERGENCE OF
MEASURES ,.... 421 UNIFORM TIGHTNESS 425, APPLICATION: DONSKER S THEOREM
426 A.5 ANALYTIC SETS AND CAPACITY . 432 APPLICATIONS TO STOCHASTIC
ANALYSIS 436, SUPPLEMENTS AND ADDITIONAL EXERCISES 440 A.6 SUSLIN
SPACES-^AND TIGHTNESS OF MEASURES 440 POLISH AND SUSLIN SPACES 440 - A.7
THE SKOROHOD TOPOLOGY 443 A.8 THE W -SPACES 448 MARCINKIEWICZ
INTERPOLATION 453, KHINTCHINE S INEQUALITIES 455, STABLE TYPE 458 X
CONTENTS A.9 SEMIGROUPS OF OPERATORS 463 RESOLVENT AND GENERATOR 463,
FELLER SEMIGROUPS 465, THE NATURAL EXTENSION OF A FELLER SEMIGROUP 467
APPENDIX B ANSWERS TO SELECTED PROBLEMS .470 REFERENCES 477 INDEX OF
NOTATIONS 483 INDEX 489 ANSWERS
HTTP://WWW.MA.UTEXAS.EDU/USERS/CUP/ANSWERS FULL INDEXES
HTTP://WWW.MA.UTEXAS.EDU/USERS/CUP/INDEXES ERRATA
HTTP://WWW.MA.UTEXAS.EDU/USERS/CUP/ERRATA
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik |
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| id | DE-604.BV014154134 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:58:37Z |
| institution | BVB |
| isbn | 0521811295 9780521811293 9780521142144 |
| language | English |
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| owner_facet | DE-739 DE-355 DE-BY-UBR DE-703 DE-91G DE-BY-TUM DE-11 DE-188 |
| physical | XIII, 501 S. Illustrationen |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Bichteler, Klaus 1938- Verfasser (DE-588)106060279 aut Stochastic integration with jumps Klaus Bichteler 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2002 XIII, 501 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 89 Hier auch später erschienene, unveränderte Nachdrucke Stochastisches Integral Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 s DE-604 Encyclopedia of mathematics and its applications 89 (DE-604)BV000903719 89 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009700319&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bichteler, Klaus 1938- Stochastic integration with jumps Encyclopedia of mathematics and its applications Stochastisches Integral Stochastisches Integral (DE-588)4126478-2 gnd |
| subject_GND | (DE-588)4126478-2 |
| title | Stochastic integration with jumps |
| title_auth | Stochastic integration with jumps |
| title_exact_search | Stochastic integration with jumps |
| title_full | Stochastic integration with jumps Klaus Bichteler |
| title_fullStr | Stochastic integration with jumps Klaus Bichteler |
| title_full_unstemmed | Stochastic integration with jumps Klaus Bichteler |
| title_short | Stochastic integration with jumps |
| title_sort | stochastic integration with jumps |
| topic | Stochastisches Integral Stochastisches Integral (DE-588)4126478-2 gnd |
| topic_facet | Stochastisches Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009700319&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT bichtelerklaus stochasticintegrationwithjumps |