Asymptotic mean-square boundedness of the numerical solutions of stochastic age-dependent population equations with Poisson jumps

Pei, Yongzhen; Yang, Haicheng; Zhang, Qimin; Shen, Fangfang

doi:10.1016/j.amc.2017.10.030

Cited by 7 publications

(5 citation statements)

References 12 publications

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“…Let Y k be the numerical solution induced by the CBE method (38). Y k is asymptotically bounded if the following inequality holds uniformly with respect to the time stepsize Δt ∈ (0, +∞):…”

Section: Asymptotic Mean-square Boundedness Analysis Of Be and Cbe Me...mentioning

confidence: 99%

“…Therefore, it is very essential to develop numerical methods and research the numerical solutions for SDEs. Until now, there have been a great many excellent results on the numerical solution of SDEs 33–38 . Mao et al 33 investigated the Euler–Maruyama scheme for a kind of SDEs which have Markovian switching and non‐Lipschitz conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Until now, there have been a great many excellent results on the numerical solution of SDEs. [33][34][35][36][37][38] Mao et al 33 investigated the Euler-Maruyama scheme for a kind of SDEs which have Markovian switching and non-Lipschitz conditions. Wang et al 34 presented the mean-square stability semi-implicit Euler method for a class of SDEs with nonlinear neutral and delay.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic mean‐square boundedness of the numerical solutions for stochastic complex‐valued neural networks with jumps

Yang²,

Wang

et al. 2022

Math Methods in App Sciences

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The paper devoted to asymptotic mean-square boundedness of several numerical methods for stochastic complex-valued neural networks with Poisson jumps.The definition of asymptotic mean-square boundedness of the numerical solution is presented, and some sufficient conditions for the underlying systems which are asymptotic mean-square boundedness are derived. By taking the advantage of the compensated split-step backward Euler (CSSBE) method and compensated backward Euler (CBE) method, sufficient criteria promising the asymptotic mean-square boundedness of CVNNs without any restriction on time stepsize, while the split-step backward Euler (SSBE) method and backward Euler (BE) method can derive asymptotic mean-square boundedness under a time stepsize constraint. The obtained theoretical results show that the compensated numerical methods own an incredible advantage over the noncompensated numerical methods on the part of asymptotic mean-square boundedness. Finally, an example is proposed and analyzed to demonstrate the effectiveness and feasibility of the proposed results.

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Section: Asymptotic Mean-square Boundedness Analysis Of Be and Cbe Me...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotic mean‐square boundedness of the numerical solutions for stochastic complex‐valued neural networks with jumps

Yang²,

Wang

et al. 2022

Math Methods in App Sciences

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“…Rathinasamy et al [9] developed the split-step method for it. For more papers in that case, we can refer to [10][11][12][13][14].…”

Section: P Tmentioning

confidence: 99%

A new convergence and positivity analysis of balanced Euler method for stochastic age‐dependent population equations

Tan

Mayavel

Rathinasamy

et al. 2020

Numerical Methods Partial

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In a previous paper, a numerical method preserving positivity was constructed for stochastic age‐dependent population equations. However, only the local error of the balanced Euler method was verified. In this paper, we will give the global error of this numerical method in the mean square sense. Moreover, the strong convergence order is investigated which proves the convergence of the aforementioned method with strong order p=12 in the mean of global error. At last, we give some numerical experiments to illustrate the efficiency of our method.

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“…As an important branch of SDEs, stochastic population equations have received a great deal of attention. In the present investigation, the random behavior described by different stochastic processes such as Markovian switching, Poisson jumps, and fractional Brownian motion is incorporated into the stochastic age-dependent population equations (SAPEs) (see e.g., [10,11,18,19,22,28]). In these population dynamics, one assumes that the system is governed by a principle of causality, that is the future state of the system is determined solely by the present states.…”

Section: Introductionmentioning

confidence: 99%

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

Deng

Fei

Liang

et al. 2019

Applied Numerical Mathematics

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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 switching. We show that the numerical method is convergent under the given conditions. Numerical examples are provided to illustrate our results.

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Asymptotic mean-square boundedness of the numerical solutions of stochastic age-dependent population equations with Poisson jumps

Cited by 7 publications

References 12 publications

Asymptotic mean‐square boundedness of the numerical solutions for stochastic complex‐valued neural networks with jumps

Asymptotic mean‐square boundedness of the numerical solutions for stochastic complex‐valued neural networks with jumps

A new convergence and positivity analysis of balanced Euler method for stochastic age‐dependent population equations

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

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