Reflecting Stochastic Differential Equations with Jumps and Applications: 408 (Chapman & Hall/CRC Research Notes in Mathematics Series) - Softcover

Rong, Situ

Softcover

ISBN 10: 1584881259 ISBN 13: 9781584881254

Publisher: Chapman and Hall/CRC, 1999

Synopsis

Many important physical variables satisfy certain dynamic evolution systems and can take only non-negative values. Therefore, one can study such variables by studying these dynamic systems. One can put some conditions on the coefficients to ensure non-negative values in deterministic cases. However, as a random process disturbs the system, the components of solutions to stochastic differential equations (SDE) can keep changing between arbitrary large positive and negative values-even in the simplest case. To overcome this difficulty, the author examines the reflecting stochastic differential equation (RSDE) with the coordinate planes as its boundary-or with a more general boundary. Reflecting Stochastic Differential Equations with Jumps and Applications systematically studies the general theory and applications of these equations. In particular, the author examines the existence, uniqueness, comparison, convergence, and stability of strong solutions to cases where the RSDE has discontinuous coefficients-with greater than linear growth-that may include jump reflection. He derives the nonlinear filtering and Zakai equations, the Maximum Principle for stochastic optimal control, and the necessary and sufficient conditions for the existence of optimal control. Most of the material presented in this book is new, including much new work by the author concerning SDEs both with and without reflection. Much of it appears here for the first time. With the application of RSDEs to various real-life problems, such as the stochastic population and neurophysiological control problems-both addressed in the text-scientists dealing with stochastic dynamic systems will find this an interesting and useful work.

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Review

"The author tries to obtain the weakest assumptions in his theorems, so this should be of interest to specialists who have to deal with systems with unusual conditions." -J. Picard, Zentralblatt MATH Vol. 942 Promo Copy

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 1999
• Language: English
• ISBN 10: 1584881259
• ISBN 13: 9781584881254
• Binding: Paperback
• Edition number: 1
• Number of pages: 224