Random Perturbation Methods with Applications in Science and Engineering - Anatoli V. Skorokhod

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Résumé :
This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.

Biographie:
Biography of I.I. Gikhman Iosif Ilyich Gikhman was born on the 26^th of May 1918 in the city of Uman, Ukraine. He studied in Kiev, graduating in 1939, then remained there to teach and do research under the supervision of N. Bogolyubov, defending a candidate thesis on the influence of random processes on dynamical systems in 1942 and a doctoral dissertation on Markov processes and mathematical statistics in 1955. I.I. Gikhman is one of the founders of the theory of stochastic differential equations and also contributed significantly to mathematical statistics, limit theorems, multidimensional martingales, and stochastic control. He died in 1985, in Donetsk. Biography of A.V. Skorokhod Anatoli Vladimirovich Skorokhod was born on September 10^th, 1930 in the city Nikopol, Ukraine. He graduated from Kiev University in 1953, after which his graduate studies at Moscow University, were directed by E.B. Dynkin. From 1956 to 1964 Anatoli Skorokhod was a professor of Kiev university. Threafter he worked at the Institute of Mathematics of the Ukrainian Academy of Science, but he has also, since 1993, been professor of Statistics and Probability at Michigan State University. Skorokhod was elected to the Ukrainian Academy of Sciences in 1985 and became a Fellow of American Academy of Arts and Sciences in 2000. His mathematical research interests are the theory of stochastic processes, stochastic differential equations, Markov processes, randomly perturbed dynamical systems....

Sommaire:
This book covers the impact of noise on models that are widely used in science and engineering, and applies perturbed methods which assume noise changes on a faster time or space scale than the system being studied. The book is written in two parts. The first part carefully develops mathematical methods of studying random perturbations of dynamical systems. The second part presents non-random problems, reformulated to account for both external and system random noise, and analyzed using results from Part I. Researchers and graduate students in mathematics and engineering will find this book useful....