Verfügbarkeit: Continuous martingales and Brownian motion

Continuous martingales and Brownian motion:

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Bibliographische Detailangaben
Beteiligte Personen:	Revuz, Daniel 1936- (VerfasserIn), Yor, Marc 1949-2014 (VerfasserIn)
Format:	Buch
Sprache:	Deutsch
Veröffentlicht:	Berlin [u.a.] Springer 1999
Ausgabe:	3. ed.
Schriftenreihe:	Die Grundlehren der mathematischen Wissenschaften 293
Schlagwörter:	Brownian motion processes Martingales (Mathematics) Stochastische Analysis Stochastischer Prozess Martingal Brownsche Bewegung Martingaltheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008359796&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XIII, 602 S.
ISBN:	3540643257

Internformat

MARC


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Datensatz im Suchindex

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adam_text	Table of Contents Chapter 0. Preliminaries 1 § 1. Basic Notation 1 §2. Monotone Class Theorem 2 §3. Completion 3 §4. Functions of Finite Variation and Stieltjes Integrals 4 §5. Weak Convergence in Metric Spaces 9 §6. Gaussian and Other Random Variables 11 Chapter I. Introduction 15 § 1. Examples of Stochastic Processes. Brownian Motion 15 §2. Local Properties of Brownian Paths 26 §3. Canonical Processes and Gaussian Processes 33 §4. Filtrations and Stopping Times 41 Notes and Comments 48 Chapter II. Martingales 51 § 1. Definitions, Maximal Inequalities and Applications 51 §2. Convergence and Regularization Theorems 60 §3. Optional Stopping Theorem 68 Notes and Comments 77 Chapter III. Markov Processes 79 § 1. Basic Definitions 79 §2. Feller Processes 88 §3. Strong Markov Property 102 §4. Summary of Results on Levy Processes 114 Notes and Comments 117 Chapter IV. Stochastic Integration 119 §1. Quadratic Variations 119 §2. Stochastic Integrals 137 XII Table of Contents §3. Ito s Formula and First Applications 146 §4. Burkholder Davis Gundy Inequalities 160 §5. Predictable Processes 171 Notes and Comments 176 Chapter V. Representation of Martingales 179 § 1. Continuous Martingales as Time changed Brownian Motions 179 §2. Conformal Martingales and Planar Brownian Motion 189 §3. Brownian Martingales 198 §4. Integral Representations 209 Notes and Comments 216 Chapter VI. Local Times 221 § 1. Definition and First Properties 221 §2. The Local Time of Brownian Motion 238 §3. The Three Dimensional Bessel Process 251 §4. First Order Calculus 260 §5. The Skorokhod Stopping Problem 269 Notes and Comments 277 Chapter VII. Generators and Time Reversal 281 §1. Infinitesimal Generators 281 §2. Diffusions and Ito Processes 293 §3. Linear Continuous Markov Processes 300 §4. Time Reversal and Applications 312 Notes and Comments 322 Chapter VIII. Girsanov s Theorem and First Applications 325 § 1. Girsanov s Theorem 325 §2. Application of Girsanov s Theorem to the Study of Wiener s Space 338 §3. Functionals and Transformations of Diffusion Processes 349 Notes and Comments 362 Chapter IX. Stochastic Differential Equations 365 § 1. Formal Definitions and Uniqueness 365 §2. Existence and Uniqueness in the Case of Lipschitz Coefficients 375 §3. The Case of Holder Coefficients in Dimension One 388 Notes and Comments 399 Chapter X. Additive Functionals of Brownian Motion 401 § 1. General Definitions 401 Table of Contents XIII §2. Representation Theorem for Additive Functionals of Linear Brownian Motion 409 §3. Ergodic Theorems for Additive Functionals 422 §4. Asymptotic Results for the Planar Brownian Motion 430 Notes and Comments 436 Chapter XI. Bessel Processes and Ray Knight Theorems 439 §1. Bessel Processes 439 §2. Ray Knight Theorems 454 §3. Bessel Bridges 463 Notes and Comments 469 Chapter XII. Excursions 471 §1. Prerequisites on Poisson Point Processes 471 §2. The Excursion Process of Brownian Motion 480 §3. Excursions Straddling a Given Time 488 §4. Descriptions of Ito s Measure and Applications 493 Notes and Comments 511 Chapter XIII. Limit Theorems in Distribution 515 § 1. Convergence in Distribution 515 §2. Asymptotic Behavior of Additive Functionals of Brownian Motion 522 §3. Asymptotic Properties of Planar Brownian Motion 531 Notes and Comments 541 Appendix 543 § 1. Gronwall s Lemma 543 §2. Distributions 543 §3. Convex Functions 544 §4. Hausdorff Measures and Dimension 547 §5. Ergodic Theory 548 §6. Probabilities on Function Spaces 548 §7. Bessel Functions 549 §8. Sturm Liouville Equation 550 Bibliography 553 Index of Notation 591 Index of Terms 595 Catalogue 601
any_adam_object	1
author	Revuz, Daniel 1936- Yor, Marc 1949-2014
author_GND	(DE-588)120628619 (DE-588)120628635
author_facet	Revuz, Daniel 1936- Yor, Marc 1949-2014
author_role	aut aut
author_sort	Revuz, Daniel 1936-
author_variant	d r dr m y my
building	Verbundindex
bvnumber	BV012329087
classification_rvk	QH 234 SK 820
classification_tum	MAT 605f
ctrlnum	(OCoLC)40481166 (DE-599)BVBBV012329087
dewey-full	519.287
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	519 - Probabilities and applied mathematics
dewey-raw	519.287
dewey-search	519.287
dewey-sort	3519.287
dewey-tens	510 - Mathematics
discipline	Mathematik Wirtschaftswissenschaften
edition	3. ed.
format	Book
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id	DE-604.BV012329087
illustrated	Not Illustrated
indexdate	2024-12-20T10:28:21Z
institution	BVB
isbn	3540643257
language	German
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-008359796
oclc_num	40481166
open_access_boolean
owner	DE-355 DE-BY-UBR DE-384 DE-91G DE-BY-TUM DE-703 DE-824 DE-706 DE-634 DE-83 DE-188
owner_facet	DE-355 DE-BY-UBR DE-384 DE-91G DE-BY-TUM DE-703 DE-824 DE-706 DE-634 DE-83 DE-188
physical	XIII, 602 S.
publishDate	1999
publishDateSearch	1999
publishDateSort	1999
publisher	Springer
record_format	marc
series	Die Grundlehren der mathematischen Wissenschaften
series2	Die Grundlehren der mathematischen Wissenschaften
spellingShingle	Revuz, Daniel 1936- Yor, Marc 1949-2014 Continuous martingales and Brownian motion Die Grundlehren der mathematischen Wissenschaften Brownian motion processes Martingales (Mathematics) Stochastische Analysis (DE-588)4132272-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Martingal (DE-588)4126466-6 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Martingaltheorie (DE-588)4168982-3 gnd
subject_GND	(DE-588)4132272-1 (DE-588)4057630-9 (DE-588)4126466-6 (DE-588)4128328-4 (DE-588)4168982-3
title	Continuous martingales and Brownian motion
title_auth	Continuous martingales and Brownian motion
title_exact_search	Continuous martingales and Brownian motion
title_full	Continuous martingales and Brownian motion Daniel Revuz ; Marc Yor
title_fullStr	Continuous martingales and Brownian motion Daniel Revuz ; Marc Yor
title_full_unstemmed	Continuous martingales and Brownian motion Daniel Revuz ; Marc Yor
title_short	Continuous martingales and Brownian motion
title_sort	continuous martingales and brownian motion
topic	Brownian motion processes Martingales (Mathematics) Stochastische Analysis (DE-588)4132272-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Martingal (DE-588)4126466-6 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Martingaltheorie (DE-588)4168982-3 gnd
topic_facet	Brownian motion processes Martingales (Mathematics) Stochastische Analysis Stochastischer Prozess Martingal Brownsche Bewegung Martingaltheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008359796&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000395
work_keys_str_mv	AT revuzdaniel continuousmartingalesandbrownianmotion AT yormarc continuousmartingalesandbrownianmotion

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