Translations of Mathematical Monographs 1989; 339 pp; softcover Volume: 78 ISBN10: 0821846868 ISBN13: 9780821846865 List Price: US$114 Member Price: US$91.20 Order Code: MMONO/78.S
 Written by one of the foremost Soviet experts in the field, this book is intended for specialists in the theory of random processes and its applications. The author's 1982 monograph on stochastic differential equations, written with Iosif Il'ich Gikhman, did not include a number of topics important to applications. The present work begins to fill this gap by investigating the asymptotic behavior of stochastic differential equations. The main topics are ergodic theory for Markov processes and for solutions of stochastic differential equations, stochastic differential equations containing a small parameter, and stability theory for solutions of systems of stochastic differential equations. Table of Contents Ergodic theorems  General ergodic theorems
 Densities for transition probabilities and resolvents for Markov solutions of stochastic differential equations
 Ergodic theorems for onedimensional stochastic equations
 Ergodic theorems for solutions of stochastic equations in \(R^d\)
Asymptotic behavior of systems of stochastic equations containing a small parameter  Equations with a small righthand side
 Processes with rapid switching
 Averaging over variables for systems of stochastic differential equations
Stability. Linear systems  Stability of sample paths of homogeneous Markov processes
 Linear equations in \(R^d\) and the stochastic semigroups connected with them. Stability
 Stability of solutions of stochastic differential equations
Linear stochastic equations in Hilbert space. Stochastic semigroups. Stability  Linear equations with bounded coefficients
 Strong stochastic semigroups with second moments
 Stability
 Bibliography
