Stability and Moment Boundedness of the Stochastic Linear Age-structured Model
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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.
KeywordsStochastic age-structured model Stochastic stability Moment boundedness
Mathematics Subject Classification37H10 34F05 34K30 34D20
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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