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

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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 languageEnglish
Number of pages25
JournalApplied Numerical Mathematics
Publication statusAccepted/In press - 2 Jan 2019

Keywords

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

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