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.
Inhalt
Preface
Acknowledgments
Notation
1 Stochastic Integral With Respect To p-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 p*-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