Stochastic Processes: General Theory

1. Front Matter

   Pages i-xii

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2. Introduction and foundations

   • M. M. Rao

   Pages 1-60

3. Conditioning and martingales

   • M. M. Rao

   Pages 61-163

4. Stochastic function theory

   • M. M. Rao

   Pages 165-231

5. Refinements in martingale analysis

   • M. M. Rao

   Pages 233-331

6. Martingale decompositions and integration

   • M. M. Rao

   Pages 333-443

7. Stochastic integrals and differential systems

   • M. M. Rao

   Pages 445-537

8. Stochastic analysis on differential structures

   • M. M. Rao

   Pages 539-587

9. Back Matter

   Pages 589-627

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Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested.
The book is a completely revised and enlarged version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material.
Audience: Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.

• Martingal
• Martingale
• Parameter
• stochastic differential equation
• stochastic processes
• ordinary differential equations

• University of California, USA

  M. M. Rao

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