Euler–Maruyama scheme for Caputo stochastic fractional differential equations

Doàn, Thái Son; Huong, P.T.; Kloeden, Peter E.; Vu, Anh My

doi:10.1016/j.cam.2020.112989

Cited by 37 publications

(15 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the SVIEs with doubly singular kernels, Dai and Xiao [34] analysed the strong convergence order of EM method, and constructed the fast EM method to improve the computational effciency. In addition, Li et al [36] also discussed asymptotic sparation for SVIEs with doubly singular kernels, which extends the corresponding result of [35].…”

Section: Introductionsupporting

confidence: 53%

Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion

sci¹

2022

AAMM

View full text Add to dashboard Cite

Section: Introductionsupporting

confidence: 53%

Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion

sci¹

2022

AAMM

View full text Add to dashboard Cite

“…here and in the rest of the proof, M represents a positive constant independent of m, δ and h. Next, we focus on estimating the first term on the right side of (12). According to Hölder's inequality, it follows from the formulae ( 4) and ( 10) that…”

Section: Continuous Dependence Of Solutions On the Initial Valuementioning

confidence: 99%

“…On the other hand, in order to capture ubiquitous noise factors in the actual situation, stochastic integro-differential equations emerge in anomalous diffusion [29], stochastic feedback system [35] and option pricing [8]. Nowadays, more and more scholars focus on stochastic fractional equations [2,12,37,41] since it can be applied to explore the memory, hereditary and hidden properties of some noise systems in physics [24], mathematical finance [13] and ecological epidemiology [34,42], etc.…”

mentioning

confidence: 99%

Stochastic fractional integro-differential equations with weakly singular kernels: Well-posedness and Euler–Maruyama approximation

Dai

Xiao

2022

DCDS-B

View full text Add to dashboard Cite

<p style='text-indent:20px;'>This paper considers the initial value problem of general nonlinear stochastic fractional integro-differential equations with weakly singular kernels. Our effort is devoted to establishing some fine estimates to include all the cases of Abel-type singular kernels. Firstly, the existence, uniqueness and continuous dependence on the initial value of the true solution under local Lipschitz condition and linear growth condition are derived in detail. Secondly, the Euler–Maruyama method is developed for solving numerically the equation, and then its strong convergence is proven under the same conditions as the well-posedness. Moreover, we obtain the accurate convergence rate of this method under global Lipschitz condition and linear growth condition. In particular, the Euler–Maruyama method can reach strong first-order superconvergence when <inline-formula><tex-math id="M1">\begin{document}$ \alpha = 1 $\end{document}</tex-math></inline-formula>. Finally, several numerical tests are reported for verification of the theoretical findings.</p>

show abstract

“…The fractional-order- stochastic SV 1 V 2 EIRF model of order α , obtained in Equations (9-15), is a fractional-order stochastic system of differential equations and has the general form indicated in Equation (20). We can solve Equation (20) numerically using the iterative formula of the Euler-Maruyama method for

as indicated in Equation (21) [27] .

…”

Section: Numerical Algorithmsmentioning

confidence: 99%

COVID-19 deterministic and stochastic modelling with optimized daily vaccinations in Saudi Arabia

Omar¹,

Alnafisah²,

Elbarkouky³

et al. 2021

Results in Physics

View full text Add to dashboard Cite

In this paper, we investigate the stochastic nature of the COVID-19 temporal dynamics by generating a fractional-order dynamic model and a fractional-order-stochastic model. Initially, we considered the first and second vaccination doses as multiple vaccinations were initiated worldwide. The concerned models are then tested for the Saudi Arabia second virus wave, which is assumed to start on 1st March 2021. Four daily vaccination scenarios for the first and second dose are assumed for 100 days from the wave beginning. One of these scenarios is based on function optimization using the invasive weed optimization algorithm (IWO). After that, we numerically solve the established models using the fractional Euler method and the Euler-Murayama method. Finally, the obtained virus dynamics using the assumed scenarios and the real one started by the government are compared. The optimized scenario using the IWO effectively minimizes the predicted cumulative wave infections with a 4.4 % lower number of used vaccination doses.

show abstract

Euler–Maruyama scheme for Caputo stochastic fractional differential equations

Cited by 37 publications

References 8 publications

Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion

Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion

Stochastic fractional integro-differential equations with weakly singular kernels: Well-posedness and Euler–Maruyama approximation

COVID-19 deterministic and stochastic modelling with optimized daily vaccinations in Saudi Arabia

Contact Info

Product

Resources

About