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Journal of Dynamics and Differential Equations

, Volume 31, Issue 4, pp 2109–2125 | Cite as

Stability and Moment Boundedness of the Stochastic Linear Age-structured Model

  • Zhen Wang
  • Xiong LiEmail author
Article

Abstract

In this paper we study the stability and moment boundedness of the solutions to the stochastic linear age-structured model. For the linear age-structured model with general noise, the stability of the first moment is identical to that of the corresponding deterministic age-structured model. However, the stability and boundedness of the second moment are complicated and depend on the stochastic terms. For the linear age-structured model with the additive noise, we first give the explicit expression of the second moment by the Laplace transform in Itô-Doob integral, and then establish the sufficient conditions for boundedness and unboundedness of the second moment through the supremum of the real parts of all characteristic roots.

Keywords

Stochastic age-structured model Stochastic stability Moment boundedness 

Mathematics Subject Classification

37H10 34F05 34K30 34D20 

Notes

Acknowledgements

We would like to thank the referee for his/her valuable comments and suggestions that greatly improve the presentation of this work.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsHefei University of TechnologyHefeiPeople’s Republic of China
  2. 2.School of Mathematical SciencesBeijing Normal UniversityBeijingPeople’s Republic of China

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