Stochastic integration with jumps

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Stochastic integration with jumps / Klaus Bichteler

資料種別:: 図書
出版情報:: Cambridge : Cambridge University Press, 2002
形態:: xiii, 501 p. ; 24 cm
シリーズ名:: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 89 <BA00064663>
著者名:: Bichteler, Klaus <DA01785521>
ISBN:: 9780521811293 [0521811295]
書誌ID:: BA56729986

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注記:

Bibliography: p. 477-482
Includes indexes

主題:

Jump processes; Stochastic Integrals

言語:

英語

目次情報:

Preface

Introduction / Chapter 1：

Motivation: Stochastic Differential Equations / 1.1：

Wiener Process / 1.2：

The General Model / 1.3：

Integrators and Martingales / Chapter 2：

The Elementary Stochastic Integral / 2.1：

The Semivariations / 2.2：

Path Regularity of Integrators / 2.3：

Processes of Finite Variation / 2.4：

Martingales / 2.5：

Extension of the Integral / Chapter 3：

The Daniell Mean / 3.1：

The Integration Theory of a Mean / 3.2：

Countable Additivity in p-Mean / 3.3：

Measurability / 3.4：

Predictable and Previsible Processes / 3.5：

Special Properties of Daniell's Mean / 3.6：

The Indefinite Integral / 3.7：

Functions of Integrators / 3.8：

Ito's Formula / 3.9：

Random Measures / 3.10：

Control of Integral and Integrator / Chapter 4：

Change of Measure--Factorization / 4.1：

Martingale Inequalities / 4.2：

The Doob-Meyer Decomposition / 4.3：

Semimartingales / 4.4：

Previsible Control of Integrators / 4.5：

Levy Processes / 4.6：

Stochastic Differential Equations / Chapter 5：

Existence and Uniqueness of the Solution / 5.1：

Stability: Differentiability in Parameters / 5.3：

Pathwise Computation of the Solution / 5.4：

Weak Solutions / 5.5：

Stochastic Flows / 5.6：

Semigroups, Markov Processes, and PDE / 5.7：

Complements to Topology and Measure Theory / Appendix A：

Notations and Conventions / A.1：

Topological Miscellanea / A.2：

Measure and Integration / A.3：

Weak Convergence of Measures / A.4：

Analytic Sets and Capacity / A.5：

Suslin Spaces and Tightness of Measures / A.6：

The Skorohod Topology / A.7：

The L[superscript p]-Spaces / A.8：

Semigroups of Operators / A.9：

Answers to Selected Problems / Appendix B：

References

Index of Notations

Index

Answers

Full Indexes

Errata

Preface

Introduction / Chapter 1：

Motivation: Stochastic Differential Equations / 1.1：

Wiener Process / 1.2：

The General Model / 1.3：

Integrators and Martingales / Chapter 2：

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