On the decay rate for a stochastic delay differential equation with an unbounded delay

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Yao, Xin and You, Surong and Mao, Wei and Mao, Xuerong (2025) On the decay rate for a stochastic delay differential equation with an unbounded delay. Applied Mathematics Letters, 166. 109541. ISSN 0893-9659 (https://doi.org/10.1016/j.aml.2025.109541)

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Abstract

How does the delay function affect its decay rate for a stable stochastic delay differential equation with an unbounded delay? Under suitable Khasminskii-type conditions, an existence-and-uniqueness theorem for an SDDE with a general unbounded time-varying delay will be firstly given. Its decay rate will be discussed when the equation is stable. Given the unbounded delay function, it will be shown that the decay rate can be directly expressed as a function of the delay.

ORCID iDs

Yao, Xin, You, Surong, Mao, Wei and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
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