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

Xin Yao; Surong You; Wei Mao; Xuerong Mao

doi:10.1016/j.aml.2025.109541

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

Xin Yao, Surong You^*, Wei Mao, Xuerong Mao

^*Corresponding author for this work

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	109541
Journal	Applied Mathematics Letters
Volume	166
Early online date	15 Mar 2025
DOIs	https://doi.org/10.1016/j.aml.2025.109541
Publication status	Published - Jul 2025

Funding

W. Mao would like to thank the National Natural Science Foundation of China (11401261), the Qing Lan Project of Jiangsu Province for their financial support. X. Mao was supported by Royal Society of Edinburgh, United Kingdom (RSE1832) and Engineering and Physical Sciences Research Council, United Kingdom (EP/W522521/1).

Keywords

Khasminskii-type condition
stable
decay rate
Stochastic differential delay equations

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10.1016/j.aml.2025.109541

Yao-etal-2025-On-the-decay-rate-for-a-stochastic-delay-differential-equation-with-an-unbounded-delay
For the purposes of open access, a CC BY 4.0 licence has been applied to this document
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Cite this

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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.",

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AU - You, Surong

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AU - Mao, Xuerong

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N2 - 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.

AB - 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.

KW - Khasminskii-type condition

KW - stable

KW - decay rate

KW - Stochastic differential delay equations

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

Abstract

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Maths Research Associates 2021 Strathclyde

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

Abstract

Funding

Keywords

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Maths Research Associates 2021 Strathclyde

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