Yousef Alnafisah

Bio: Yousef Alnafisah is an academic researcher from Qassim University. The author has contributed to research in topics: Stochastic differential equation & Milstein method. The author has an hindex of 2, co-authored 7 publications receiving 8 citations.

COVID-19 Deterministic and Stochastic Modelling with Optimized Daily Vaccinations in Saudi Arabia.

Abstract: 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.

The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method

Abstract: Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two-dimensional stochastic differential equation (SDE) using Matlab program. Our numerical experiments use Matlab to show how our truncation of Ito’-Taylor expansion at an appropriate point produces Milstein method for the SDE.

The implementation of approximate coupling in two-dimensional SDEs with invertible diffusion terms

Abstract: We explain and prove some lemmas of the approximate coupling and we give some details of the Matlab implementation of this method A particular invertible SDEs is used to show the convergence result for this method for general d, which will give an order one error bounds

Neutral delay Hilfer fractional integrodifferential equations with fractional brownian motion

Abstract: In this paper, we study the existence and uniqueness of mild solutions for neutral delay Hilfer fractional integrodifferential equations with fractional Brownian motion. Sufficient conditions for controllability of neutral delay Hilfer fractional differential equations with fractional Brownian motion are established. The required results are obtained based on the fixed point theorem combined with the semigroup theory, fractional calculus and stochastic analysis. Finally, an example is given to illustrate the obtained results.

Exact Coupling Method for Stratonovich Stochastic Differential Equation Using Non-Degeneracy for the Diffusion

Abstract: The method of Davie’s [5] describes an easily generated scheme based on the standard order-one Milstein scheme, which is order-one in the Vaserstein metric, provided that the stochastic differential equation has invertible diffusion term. We apply the exact coupling method from Davie’s paper to Stratonovich stochastic differential equation and the convergence of this method is proved by MATLAB implementation. We examine the strong convergence for the Stratonovich SDE using a particular invertible SDE.

Stochastic Differential Equations

Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

The approximation of multiple stochastic integrals

Abstract: A method for approximating the multiple stochastic integrals appearing in stochaslic Taylor expansions is proposed. It is based on a series expansion of the Brownian bridge process. Some higher order time discrete approximations for the simulation of Ito processes using these approximate multiple stochastic integrals arc also included.

Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay

Abstract: In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Caratheodory approximation approach and stochastic calculus to present the existence and uniqueness theorem of the stochastic system under Caratheodory-type conditions with Lipschitz and non-Lipschitz conditions as special cases. Some existing results are generalized and enhanced. Finally, an application is offered to illustrate the obtained theoretical results.

Mixed Neutral Caputo Fractional Stochastic Evolution Equations with Infinite Delay: Existence, Uniqueness and Averaging Principle

Abstract: The aim of this article is to consider a class of neutral Caputo fractional stochastic evolution equations with infinite delay (INFSEEs) driven by fractional Brownian motion (fBm) and Poisson jumps in Hilbert space. First, we establish the local and global existence and uniqueness theorems of mild solutions for the aforementioned neutral fractional stochastic system under local and global Carathéodory conditions by using the successive approximations, stochastic analysis, fractional calculus, and stopping time techniques. The obtained existence result in this article is new in the sense that it generalizes some of the existing results in the literature. Furthermore, we discuss the averaging principle for the proposed neutral fractional stochastic system in view of the convergence in mean square between the solution of the standard INFSEEs and that of the simplified equation. Finally, the obtained averaging theory is validated with an example.