Control theory and the calculus of variations

Science & Math

A. V. Balakrishnan

Mathematics

Academic Press

<p>The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. The book proposes to the reader whose background knowledge is limited to undergraduate level methods for engineering and physics, and easily accessible introductions to SDE and then applications as well as the numerical methods for dealing with them. To help the reader develop an intuitive understanding and hand-on numerical skills, numerous exercises including PC-exercises are included.</p>

Numerical Solution of Stochastic Differential Equations (Applications of Mathematics)

Peter E. Kloeden

Eckhard Platen

Marc Yor

I. Karatzas

Springer, Verlag

<p>Excerpt from the Preface: This is a textbook intended for a one-quarter (or one-semester, depending on the pace) course at the graduate level in Engineering.  The prerequisites are Elementary Stochastic Process theory. As a textbook, it does not purport to be a compendium of all known work on the subject. Neither is it a "trade book." Rather it attempts a logically sequenced set of topics of proven pedagogical value, emphasizing theory while not devoid of practical utility.  It develops those aspects of Kalman Filtering lore which can be given a firm mathematical basis.   The first two capters cover review material on State-Space theory and Signal (Random Process) theory - necessary but not sufficient for the sequel. The third chapter deals with Statistical Estimation theory, the mathematical framework on which Kalman Filtering rests. The main chapter is the fourth chapter dealing with the subject matter per se.  The book concludes with a chapter on Likelihood Ratios in which the Kalman filter formulation plays and essential role.  We only consider discrete-time models throughout, since all Kalman filter implementation envisaged involves digital computation.</p>

Kalman Filtering Theory (University Series in Modern Engineering)

Springer

Kalman Filtering Theory (Series in Communication and Control Systems)

Optimization Software

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Books by A. V. Balakrishnan