### 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 |
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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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## Cite this

Deng, S., Fei, W., Liang, Y., & Mao, X. (Accepted/In press). Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay.

*Applied Numerical Mathematics*.