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Limits theorems for stochastic processes/ Jean Jacod and Albert N. Shiryaev

By: Jacod, JeanContributor(s): Shiryaev, Albert NMaterial type: Text

TextSeries: (Grundlehren der mathematischen Wissenschaften) ; 288Publication details: New York: Springer, 2003Edition: 2nd edDescription: xx, 660 p. ; 24 cmISBN: 9783540439325Subject(s): Semimartingales | Limit theorems -- Probability theory | MathematicsDDC classification: 519.23

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.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode	Item holds
General Books	Central Library, Sikkim University General Book Section	519.23 JAC/ (Browse shelf(Opens below))	Available		P25267

Total holds: 0

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.

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