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Stochastic integration with jumps / Klaus Bichteler.

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

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Bibliographic Details
Online Access: Full Text (via Cambridge)
Main Author: Bichteler, Klaus
Format: Electronic eBook
Language:English
Published: Cambridge, UK ; New York : Cambridge University Press, 2002.
Series:Encyclopedia of mathematics and its applications.
Subjects:
Stochastic integrals.
Jump processes.
Table of 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.

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