Stochastic Differential Systems I

1. Front Matter

   Pages I-V

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2. Preliminaries: Stochastic Processes

   • A. V. Balakrishnan

   Pages 1-10

3. Linear Stochastic Equations

   • A. V. Balakrishnan

   Pages 11-46

4. Conditional Expectation and Martingale Theory

   • A. V. Balakrishnan

   Pages 47-68

5. Radon-Nikodym Derivatives with Respect to Wiener Measure

   • A. V. Balakrishnan

   Pages 69-85

6. The Ito Integral

   • A. V. Balakrishnan

   Pages 86-114

7. Linear Recursive Estimation

   • A. V. Balakrishnan

   Pages 115-162

8. Linear Stochastic Control

   • A. V. Balakrishnan

   Pages 163-191

9. System Identification

   • A. V. Balakrishnan

   Pages 192-222

10. Back Matter

    Pages 223-254

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This book is an outgrowth of a graduate course by the same title given at UCLA (System Science Department). presenting a Functional Analysis approach to Stochastic Filtering and Control Problems. As the writing progressed. several new points of view were developed and as a result the present work is more in the nature of a monograph on the subject than a distilled compendium of extant works. The subject of this volume is at the heart of the most used part of modern Control Theory - indeed. the bread-and-butter part. It includes the Linear (Bucy-Kalman) Filter Theory. the Feedback Control (regulation and trz.cking) Theory for plants with random disturbances. and Stochastic DifEerential Games. Linear Filter Theory is developed by a 3-Martingale approach and is perhaps the sleekest one to date. We hasten to add that although the terITlS are Engineering-oriented. and a background in Control Engineering is essential to understand the motiva­ tion. the work is totally mathematical. and in fact our aim is a rigorous mathematical presentation that is at once systematic. We begin with some preliminary necessary notions relating to Stochastic Processes. We follow Parthasarathy's work in inducing Wiener measure on the Banach Space of Continuous functions. We introduce the linear Stochastic integrals right away. We are then ready to treat linear Stochastic Differential Equations. We then look at the measures induced.

• Mathematica
• calculus
• control
• identification
• time

• System Science Department, School of Engineering and Applied Sciences, University of California, Los Angeles, USA

  A. V. Balakrishnan

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