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Asymptotic Methods in the Theory of Stochastic Differential Equations
A. V. Skorokhod
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Translations of Mathematical Monographs
1989; 339 pp; softcover
Volume: 78
ISBN-10: 0-8218-4686-8
ISBN-13: 978-0-8218-4686-5
List Price: US$114
Member Price: US$91.20
Order Code: MMONO/78.S
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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 one-dimensional 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 right-hand 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
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