Stochastic Integration

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.

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