The Resource Limit theorems for stochastic processes, Jean Jacod, Albert N. Shiryaev

Limit theorems for stochastic processes, Jean Jacod, Albert N. Shiryaev

Label
Limit theorems for stochastic processes
Title
Limit theorems for stochastic processes
Statement of responsibility
Jean Jacod, Albert N. Shiryaev
Creator
Contributor
Subject
Language
eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Jacod, Jean
Index
index present
LC call number
QA274.5
LC item number
.J33 2003
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
Shiri︠a︡ev, A. N.
http://library.link/vocab/subjectName
  • Semimartingales (Mathematics)
  • Limit theorems (Probability theory)
  • Semimartingales (Mathématiques)
  • Théorèmes limites (Théorie des probabilités)
  • Limit theorems (Probability theory)
  • Semimartingales (Mathematics)
  • Stochastische processen
  • Limiettheorema's
  • Semimartingal
  • Grenzwertsatz
  • Stochastischer Prozess
Label
Limit theorems for stochastic processes, Jean Jacod, Albert N. Shiryaev
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. [641]-651) and indexes
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
I. The general theory of stochastic processes, semimartingales and stochastic integrals -- 1. Stochastic basis, stopping times, optional [sigma]-field, martingales -- 2. Predictable [sigma]-field, predictable times -- 3. Increasing processes -- 4. Semimartingales and stochastic integrals -- II. Characteristics of semimartingales and processes with independent increments -- 1. Random measures -- 2. Characteristics of semimartingales -- 3. Some examples -- 4. Semimartingales with independent increments -- 5. Processes with independent increments which are not semimartingales -- 6. Process with conditionally independent increments -- 7. Progressive conditional continuous PIIs -- 8. Semimartingales, stochastic exponential and stochastic logarithm -- III. Martingale problems and changes of measures -- 1. Martingale problems and point processes -- 2. Martingale problems and semimartingales -- 3. Absolutely continuous changes of measures -- 4. Representation theorem for martingales -- 5. Absolutely continuous change of measures: Explicit computation of the density process -- 6. Integrals of vector-valued processes and [sigma]-martingales -- 7. Laplace cumulant processes and Esscher's change of measures -- IV. Hellinger processes, absolute continuity and singularity of measures -- 1. Hellinger integrals and Hellinger processes -- 2. Predictable criteria for absolute continuity and singularity -- 3. Hellinger processes for solutions of martingale problems -- 4. Examples -- V. Contiguity, entire separation, convergence in variation -- 1. Contiguity and entire separation -- 2. Predictable criteria for contiguity and entire separation -- 3. Examples -- 4. Variation metric -- VI. Skorokhod topology and convergence of processes -- 1. The Skorokhod topology -- 2. Continuity for the Skorokhod topology -- 3. Weak convergence -- 4. Criteria for tightness: The quasi-left continuous case -- 5. Criteria for tightness: The general case -- 6. Convergence, quadratic variation, stochastic integrals -- VII. Convergence of processes with independent increments -- 1. Introduction to functional limit theorems -- 2. Finite-dimensional convergence -- 3. Functional convergence and characteristics -- 4. More on the general case -- 5. The central limit theorem -- VIII. Convergence to a process with independent increments -- 1. Finite-dimensional convergence, a general theorem -- 2. Convergence to a PII without fixed time of discontinuity -- 3. Applications -- 4. Convergence to a general process with independent increments -- 5. Convergence to a mixture of PII's, stable convergence and mixing convergence -- IX. Convergence to a semimartingale -- 1. Limits of martingales -- 2. Identification of the limit -- 3. Limit theorems for semimartingales -- 4. Applications -- 5. Convergence of stochastic integrals -- 6. Stability for stochastic differential equation -- 7. Stable convergence to a progressive conditional continuous PII -- X. Limit theorems, density processes and contiguity -- 1. Convergence of the density processes to a continuous process -- 2. Convergence of the log-likelihood to a process with independent increments -- 3. The statistical invariance principle
Dimensions
24 cm.
Edition
2nd ed.
Extent
xx, 660 pages
Isbn
9783540439325
Lccn
2002030661
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
System control number
  • (OCoLC)50554399
  • (OCoLC)ocm50554399
Label
Limit theorems for stochastic processes, Jean Jacod, Albert N. Shiryaev
Publication
Bibliography note
Includes bibliographical references (p. [641]-651) and indexes
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
I. The general theory of stochastic processes, semimartingales and stochastic integrals -- 1. Stochastic basis, stopping times, optional [sigma]-field, martingales -- 2. Predictable [sigma]-field, predictable times -- 3. Increasing processes -- 4. Semimartingales and stochastic integrals -- II. Characteristics of semimartingales and processes with independent increments -- 1. Random measures -- 2. Characteristics of semimartingales -- 3. Some examples -- 4. Semimartingales with independent increments -- 5. Processes with independent increments which are not semimartingales -- 6. Process with conditionally independent increments -- 7. Progressive conditional continuous PIIs -- 8. Semimartingales, stochastic exponential and stochastic logarithm -- III. Martingale problems and changes of measures -- 1. Martingale problems and point processes -- 2. Martingale problems and semimartingales -- 3. Absolutely continuous changes of measures -- 4. Representation theorem for martingales -- 5. Absolutely continuous change of measures: Explicit computation of the density process -- 6. Integrals of vector-valued processes and [sigma]-martingales -- 7. Laplace cumulant processes and Esscher's change of measures -- IV. Hellinger processes, absolute continuity and singularity of measures -- 1. Hellinger integrals and Hellinger processes -- 2. Predictable criteria for absolute continuity and singularity -- 3. Hellinger processes for solutions of martingale problems -- 4. Examples -- V. Contiguity, entire separation, convergence in variation -- 1. Contiguity and entire separation -- 2. Predictable criteria for contiguity and entire separation -- 3. Examples -- 4. Variation metric -- VI. Skorokhod topology and convergence of processes -- 1. The Skorokhod topology -- 2. Continuity for the Skorokhod topology -- 3. Weak convergence -- 4. Criteria for tightness: The quasi-left continuous case -- 5. Criteria for tightness: The general case -- 6. Convergence, quadratic variation, stochastic integrals -- VII. Convergence of processes with independent increments -- 1. Introduction to functional limit theorems -- 2. Finite-dimensional convergence -- 3. Functional convergence and characteristics -- 4. More on the general case -- 5. The central limit theorem -- VIII. Convergence to a process with independent increments -- 1. Finite-dimensional convergence, a general theorem -- 2. Convergence to a PII without fixed time of discontinuity -- 3. Applications -- 4. Convergence to a general process with independent increments -- 5. Convergence to a mixture of PII's, stable convergence and mixing convergence -- IX. Convergence to a semimartingale -- 1. Limits of martingales -- 2. Identification of the limit -- 3. Limit theorems for semimartingales -- 4. Applications -- 5. Convergence of stochastic integrals -- 6. Stability for stochastic differential equation -- 7. Stable convergence to a progressive conditional continuous PII -- X. Limit theorems, density processes and contiguity -- 1. Convergence of the density processes to a continuous process -- 2. Convergence of the log-likelihood to a process with independent increments -- 3. The statistical invariance principle
Dimensions
24 cm.
Edition
2nd ed.
Extent
xx, 660 pages
Isbn
9783540439325
Lccn
2002030661
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
System control number
  • (OCoLC)50554399
  • (OCoLC)ocm50554399

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