Asymptotic Analysis for Functional Stochastic Differential Equations

  • Jianhai Bao
  • George Yin
  • Chenggui Yuan

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Jianhai Bao, George Yin, Chenggui Yuan
    Pages 1-25
  3. Jianhai Bao, George Yin, Chenggui Yuan
    Pages 27-54
  4. Jianhai Bao, George Yin, Chenggui Yuan
    Pages 55-75
  5. Jianhai Bao, George Yin, Chenggui Yuan
    Pages 77-111
  6. Jianhai Bao, George Yin, Chenggui Yuan
    Pages 113-128
  7. Back Matter
    Pages 129-151

About this book


This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.
This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.


Functional stochastic differential equation Ergodicity Invariant measure Uniform large deviation principle Delay Cox-Ingersoll-Ross model with jumps Long-term return Two-factor model Brownian Motion Jump process

Authors and affiliations

  • Jianhai Bao
    • 1
  • George Yin
    • 2
  • Chenggui Yuan
    • 3
  1. 1.Department of MathematicsCentral South UniversityChangshaChina
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA
  3. 3.Department MathematicsSwansea UniversitySwanseaUnited Kingdom

Bibliographic information

  • DOI
  • Copyright Information The Author(s) 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-46978-2
  • Online ISBN 978-3-319-46979-9
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site