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 journal › Article

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

Deng, Shounian ; Fei, Weiyin ; Liang, Yong ; Mao, Xuerong. / Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay. In: Applied Numerical Mathematics. 2019
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Deng, S, Fei, W, Liang, Y & Mao, X 2019, 'Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay' Applied Numerical Mathematics.

Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay. / Deng, Shounian; Fei, Weiyin; Liang, Yong; Mao, Xuerong.

In: Applied Numerical Mathematics, 02.01.2019.

Research output: Contribution to journal › Article

TY - JOUR

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

T2 - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -

Deng S, Fei W, Liang Y, Mao X. Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay. Applied Numerical Mathematics. 2019 Jan 2.