RESEARCH ARTICLE

Moderate deviation and central limit theorem for stochastic differential delay equations with polynomial growth

  • Yongqiang SUO 1,2 ,
  • Jin TAO 3 ,
  • Wei ZHANG , 1
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  • 1. School of Mathematics and Statistics, Central South University, Changsha 410083, China
  • 2. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, UK
  • 3. Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, China

Received date: 29 Mar 2017

Accepted date: 19 Jun 2018

Published date: 14 Aug 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

Abstract

Employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderate deviation for a class of stochastic differential delay equations with small noises, where the coeffcients are allowed to be highly nonlinear growth with respect to the variables. Moreover, we obtain the central limit theorem for stochastic differential delay equations which the coeffcients are polynomial growth with respect to the delay variables.

Cite this article

Yongqiang SUO , Jin TAO , Wei ZHANG . Moderate deviation and central limit theorem for stochastic differential delay equations with polynomial growth[J]. Frontiers of Mathematics in China, 2018 , 13(4) : 913 -933 . DOI: 10.1007/s11464-018-0710-3

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