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Stochastic integration with jumps

Author: Klaus Bichteler
Publisher: Cambridge, UK ; New York : Cambridge University Press, 2002.
Series: Encyclopedia of mathematics and its applications.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The complete theory of stochastic differential equations driven by jumps, their stability, and numerical approximation theories.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bichteler, Klaus.
Stochastic integration with jumps
(DLC) 2001043017
(OCoLC)47443931
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Klaus Bichteler
ISBN: 9780511020735 0511020732 9780511549878 0511549873 9781107095861 1107095867
OCLC Number: 861692903
Description: 1 online resource (xiii, 501 pages) : illustrations.
Contents: Motivation: Stochastic Differential Equations --
Wiener Process --
The General Model --
Integrators and Martingales --
The Elementary Stochastic Integral --
The Semivariations --
Path Regularity of Integrators --
Processes of Finite Variation --
Martingales --
Extension of the Integral --
The Daniell Mean --
The Integration Theory of a Mean --
Countable Additivity in p-Mean --
Measurability --
Predictable and Previsible Processes --
Special Properties of Daniell's Mean --
The Indefinite Integral --
Functions of Integrators --
Ito's Formula --
Random Measures --
Control of Integral and Integrator --
Change of Measure--Factorization --
Martingale Inequalities --
The Doob-Meyer Decomposition --
Semimartingales --
Previsible Control of Integrators --
Levy Processes --
Stochastic Differential Equations --
Existence and Uniqueness of the Solution --
Stability: Differentiability in Parameters --
Pathwise Computation of the Solution --
Weak Solutions --
Stochastic Flows --
Semigroups, Markov Processes, and PDE --
Complements to Topology and Measure Theory --
Notations and Conventions --
Topological Miscellanea --
Measure and Integration --
Weak Convergence of Measures --
Analytic Sets and Capacity --
Suslin Spaces and Tightness of Measures --
The Skorohod Topology --
The L[superscript p]-Spaces --
Semigroups of Operators.
Series Title: Encyclopedia of mathematics and its applications.
Responsibility: Klaus Bichteler.
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Abstract:

The complete theory of stochastic differential equations driven by jumps, their stability, and numerical approximation theories.  Read more...

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Review of the hardback: 'The material in the book is presented well: it is detailed, motivation is stressed throughout and the text is written with an enjoyable pinch of dry humour.' Evelyn Buckwar, Read more...

 
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