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

Deng, Shounian and Fei, Weiyin and Liang, Yong and Mao, Xuerong (2019) Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay. Applied Numerical Mathematics. ISSN 0168-9274 (In Press)

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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.