Stochastic Integration

Stochastic Integration

1st Edition - July 28, 1980

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  • Authors: Michel Metivier, J. Pellaumail
  • eBook ISBN: 9781483218786

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Description

Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Stochastic Integration focuses on the processes, methodologies, and approaches involved in stochastic integration. The publication first takes a look at the Ito formula, stochastic integral equations, and martingales and semimartingales. Discussions focus on Meyer process and decomposition theorem, inequalities, examples of stochastic differential equations, general stochastic integral equations, and applications of the Ito formula. The text then elaborates on stochastic measures, including stochastic measures and related integration and the Riesz representation theorem. The manuscript tackles the special features of infinite dimensional stochastic integration, as well as the isometric integral of a Hubert-valued square integrable martingale, cylindrical processes, and stochastic integral with respect to 2-cylindrical martingales with finite quadratic variation. The book is a valuable reference for mathematicians and researchers interested in stochastic integration.

Table of Contents


  • Preface

    Acknowledgments

    Notation

    1 Stochastic Integral With Respect To π-Processes

    1 Stochastic Basis and Processes

    Extensions and Exercises

    2 Stochastic Integral

    Extensions and Exercises

    Historical Notes

    2 The Ito Formula

    3 Ito Formula

    4 Applications of the Ito Formula

    Extensions and Exercises

    Historical Notes

    3 Stochastic Integral Equations

    5 Examples of Stochastic Differential Equations

    6 General Stochastic Integral Equations

    7 Properties of Solutions; Conditions for Nonexplosion and Stability

    Exercises

    Historical Notes

    4 Martingales And Semimartingales

    8 Martingales and Submartingales: Equi-Integrability and Tied Properties

    Extensions and Exercises

    9 Meyer Process and Decomposition Theorem

    Extensions and Examples

    10 π*-Processes and Semimartingales

    Extensions and Examples

    11 Inequalities

    Historical Notes

    5 Stochastic Measures

    12 Stochastic Measures and Related Integration

    13 Riesz Representation Theorem

    Historical Notes

    6 Special Features Of Infinite-Dimensional Stochastic Integration

    14 The Isometric Integral of a Hilbert-Valued Square Integrable Martingale

    Extensions and Comments

    15 Cylindrical Processes

    16 Stochastic Integral with Respect to 2-Cylindrical Martingales with Finite Quadratic Variation

    Historical Notes

    Bibliography

    Index

Product details

  • No. of pages: 208
  • Language: English
  • Copyright: © Academic Press 1980
  • Published: July 28, 1980
  • Imprint: Academic Press
  • eBook ISBN: 9781483218786

About the Authors

Michel Metivier

J. Pellaumail

About the Editors

Z. W. Birnbaum

E. Lukacs

Affiliations and Expertise

Bowling Green State University

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