### Abstract

Original language | English |
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Number of pages | 25 |

Journal | Applied Numerical Mathematics |

Publication status | Accepted/In press - 2 Jan 2019 |

### Fingerprint

### Keywords

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

### Cite this

*Applied Numerical Mathematics*.

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**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.

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

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -