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Frontiers of Mathematics in China

, Volume 13, Issue 4, pp 913–933 | Cite as

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

  • Yongqiang Suo
  • Jin Tao
  • Wei Zhang
Research Article
  • 7 Downloads

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 coefficients 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 coefficients are polynomial growth with respect to the delay variables.

Keywords

Stochastic differential delay equation (SDDE) polynomial growth central limit theorem moderate deviation principle weak convergence 

MSC

60F05 60F10 60H10 

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Notes

Acknowledgements

The authors are grateful to the anonymous referees for their valuable comments and corrections. This work was supported in part by the National Natural Science Foundation of China (Grant No. 11401592), the Natural Science Foundation of Hunan Province (No. 13JJ5043), and the Mathematics and Interdisciplinary Sciences Project of Central South University.

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Copyright information

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

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCentral South UniversityChangshaChina
  2. 2.Department of MathematicsSwansea UniversitySwanseaUK
  3. 3.Department of MathematicsSouthern University of Science and TechnologyShenzhenChina

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