Proportional Itô–Doob Stochastic Fractional Order Systems

Makhlouf, Abdellatif Ben; Mchiri, Lassaad; Othman, Hakeem A.; Rguigui, Hafedh; Boulaaras, Salah

doi:10.3390/math11092049

Mathematics

2023

DOI: 10.3390/math11092049

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Proportional Itô–Doob Stochastic Fractional Order Systems

Abdellatif Ben Makhlouf

Lassaad Mchiri

Hakeem A. Othman

et al.

Abstract: In this article, we discuss the existence and uniqueness of proportional Itô–Doob stochastic fractional order systems (PIDSFOS) by using the Picard iteration method. The paper provides new results using the proportional fractional integral and stochastic calculus techniques. We have shown the convergence of the solution of the averaged PIDSFOS to that of the standard PIDSFOS in the context of the mean square and also in probability. One example is given to illustrate our results.

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Nonlinear Stochastic Operators and Associated Inhomogeneous Entangled Quantum Markov Chains

Souissi,

Mukhamedov

2024

J Nonlinear Math Phys

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In the present paper, we introduce a class of F-stochastic operators on a finite-dimensional simplex, each of which is regular, ascertaining that the species distribution in the succeeding generation corresponds to the species distribution in the previous one in the long run. It is proposed a new scheme to define non-homogeneous Markov chains contingent on the F-stochastic operators and given initial data. By means of the uniform ergodicity of the non-homogeneous Markov chain, we define a non-homogeneous (quantum) entangled Markov chain. Furthermore, it is established that the non-homogeneous entangled Markov chain enables $$\psi$$ ψ -mixing property.

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Nonlinear Stochastic Operators and Associated Inhomogeneous Entangled Quantum Markov Chains

Souissi,

Mukhamedov

2024

J Nonlinear Math Phys

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EWMA control chart using Bayesian approach under paired ranked set sampling schemes: An application to reliability engineering

Khan

Noor‐ul‐Amin

Khalifa

et al. 2023

MATH

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<abstract> <p>Control charts are widely used to efficiently detect small to moderate shifts and they include exponentially moving average control charts, named memory type control charts. Today, memory type control charts are a significant tool to assure quality standards and monitor manufacturing goods. The proposed study suggests a novel Bayesian exponentially weighted moving average (EWMA) control chart design utilizing various pair ranked set sampling schemes for posterior and posterior predictive distributions given an informative prior. The proposed chart strategy is evaluated in terms of the small run length characteristic by using Monte Carlo simulation methods. The comparative analysis is also carried out by using a Bayesian EWMA control chart to apply simple random sampling for the respective average and standard deviation of the run length values in the both control chart designs. The results revealed efficient and rapid detection of shifts in process means which proves the success and superiority of the suggested design. A real-life data sets is used to elaborate the efficient application of the suggested Bay-EWMA-PRSS control chart design. The overall research findings support the theoretical and simulation results, which are provided in the form of extensive tables.</p> </abstract>

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Proportional Itô–Doob Stochastic Fractional Order Systems

Cited by 2 publications

References 36 publications

Nonlinear Stochastic Operators and Associated Inhomogeneous Entangled Quantum Markov Chains

Nonlinear Stochastic Operators and Associated Inhomogeneous Entangled Quantum Markov Chains

EWMA control chart using Bayesian approach under paired ranked set sampling schemes: An application to reliability engineering

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