Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay

Shounian Deng; Weiyin Fei; Yong Liang; Xuerong Mao

Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay

Shounian Deng, Weiyin Fei, Yong Liang, Xuerong Mao

Mathematics And Statistics

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Abstract

We present a stochastic age-dependent population model that accounts for Markovian switching and variable delay. By using the approximate value at the nearest grid-point on the left of the delayed argument to estimate the delay function, we propose a class of split-step θ -method for solving stochastic delay age-dependent population equations (SDAPEs) with Markovian switch- ing. We show that the numerical method is convergent under the given conditions. Numerical examples are provided to illustrate our results.

Original language	English
Number of pages	25
Journal	Applied Numerical Mathematics
Publication status	Accepted/In press - 2 Jan 2019

Keywords

stochastic delay age-dependent pupulation equations
stong convergence
Markovian switching
Ito formula

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Deng-etal-ANM-2018-age-dependent-population-equations-with-Markovian-switching-and-variable-delayAccepted author manuscript, 456 KBLicence: CC BY-NC-ND 4.0

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title = "Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay",

abstract = "We present a stochastic age-dependent population model that accounts for Markovian switching and variable delay. By using the approximate value at the nearest grid-point on the left of the delayed argument to estimate the delay function, we propose a class of split-step θ -method for solving stochastic delay age-dependent population equations (SDAPEs) with Markovian switch- ing. We show that the numerical method is convergent under the given conditions. Numerical examples are provided to illustrate our results.",

keywords = "stochastic delay age-dependent pupulation equations, stong convergence, Markovian switching, Ito formula",

author = "Shounian Deng and Weiyin Fei and Yong Liang and Xuerong Mao",

year = "2019",

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language = "English",

journal = "Applied Numerical Mathematics",

issn = "0168-9274",

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T1 - Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay

AU - Deng, Shounian

AU - Fei, Weiyin

AU - Liang, Yong

AU - Mao, Xuerong

PY - 2019/1/2

Y1 - 2019/1/2

N2 - We present a stochastic age-dependent population model that accounts for Markovian switching and variable delay. By using the approximate value at the nearest grid-point on the left of the delayed argument to estimate the delay function, we propose a class of split-step θ -method for solving stochastic delay age-dependent population equations (SDAPEs) with Markovian switch- ing. We show that the numerical method is convergent under the given conditions. Numerical examples are provided to illustrate our results.

AB - We present a stochastic age-dependent population model that accounts for Markovian switching and variable delay. By using the approximate value at the nearest grid-point on the left of the delayed argument to estimate the delay function, we propose a class of split-step θ -method for solving stochastic delay age-dependent population equations (SDAPEs) with Markovian switch- ing. We show that the numerical method is convergent under the given conditions. Numerical examples are provided to illustrate our results.

KW - stochastic delay age-dependent pupulation equations

KW - stong convergence

KW - Markovian switching

KW - Ito formula

M3 - Article

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -