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

Research output: Contribution to journalArticle

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.
LanguageEnglish
Number of pages25
JournalApplied Numerical Mathematics
StateAccepted/In press - 2 Jan 2019

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θ-method
Markovian Switching
Variable Delay
Dependent
Population Model
Numerical methods
Switch
Numerical Methods
Grid
Numerical Examples
Estimate
Class

Keywords

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

Cite this

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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.",
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AU - Fei,Weiyin

AU - Liang,Yong

AU - Mao,Xuerong

PY - 2019/1/2

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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.

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KW - stong convergence

KW - Markovian switching

KW - Ito formula

M3 - Article

JO - Applied Numerical Mathematics

T2 - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

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