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Stochastic integration with jumps /Klaus Bichteler.

By: Material type: TextTextSeries: Publication details: Cambridge, UK ; New York : Cambridge University Press, (c)2002.Description: 1 online resource (xiii, 501 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780511020735
  • 9780511549878
  • 9781107095861
Subject(s): Genre/Form: LOC classification:
  • QA274 .S763 2002
Online resources: Available additional physical forms:
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.
Subject: The complete theory of stochastic differential equations driven by jumps, their stability, and numerical approximation theories.
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Includes bibliographies and index.

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.

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

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