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A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 13430

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Special Issue Editor

Prof. Dr. Jewgeni H. Dshalalow

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Guest Editor

Department of Mathematical Sciences, Florida Institute of Technology, College of Engineering and Science, Melbourne, FL 32940, USA
Interests: stochastic analysis; abstract analysis; random measures; stochastic games; probabilistic applications to cell-molecular biology

Special Issue Information

Dear Colleagues,

The purpose of this Special Issue is to present the recent advances in broad areas of stochastic analysis ranging from the theoretical to the more applied, covering topics in stochastic differential equations, Itô calculus, martingales, Lévy processes, stochastic finance, random measures, random walks, fluctuation theory, stochastic geometry, statistical inference of stochastic processes, special processes, queueing theory, matrix-geometric methods, and applications of stochastics to cell-molecular biology and physical sciences. This will give the reader an idea of what stochastic analysis is about rather than focusing on specialized topics that are widely available in the literature. This Special Issue will gather experts from these areas to present their latest research. There are elements and principles of symmetry and related concepts of invariance and equivalence present in many mathematical, physical, and biological sciences that are readily identified, and they will also be included in the contributed articles.

The submitted manuscripts must fall within the scope of Symmetry.

Prof. Dr. Jewgeni H. Dshalalow
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

stochastic differential equations
applications of stochastic processes to biological sciences
random walks and fluctuations
stochastic processes in queueing and reliability
random measures
stochastic geometry
stochastic finance
queuing theory

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Published Papers (6 papers)

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Research

16 pages, 4011 KiB

Open AccessArticle

Novel Analysis between Two-Unit Hot and Cold Standby Redundant Systems with Varied Demand

by Reetu Malhotra, Faten S. Alamri and Hamiden Abd El-Wahed Khalifa

Symmetry 2023, 15(6), 1220; https://doi.org/10.3390/sym15061220 - 7 Jun 2023

Cited by 7 | Viewed by 1687

Abstract

Decisive applications, such as control systems and aerial navigation, require a standby system to meet stringent safety, availability, and reliability. The paper evaluates the availability, reliability, and other measures of system effectiveness for two stochastic models in a symmetrical way with varying demand: Model 1 (a two-unit cold standby system) and Model 2 (a two-unit hot standby system). In Model 1, the standby unit needs to be activated before it may begin to function; in Model 2, the standby unit is always operational unless it fails. The current study demonstrates that the hot standby system is more expensive than the cold standby system under two circumstances: a decrease in demand or the hot standby unit’s failure rate exceeding a predetermined threshold. The cold standby system’s activation time is at most a certain threshold, and turning both units on at once is necessary to handle the increasing demand. In that case, the hot standby will be more expensive than the cold standby system. The authors used semi-Markov and regenerative point techniques to analyze both models. They collected actual data from a cable manufacturing plant to illustrate the findings. Plotting several graphs and obtaining cut-off points make it easier to choose the standby to employ. Full article

(This article belongs to the Special Issue Stochastic Analysis with Applications and Symmetry)

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12 pages, 307 KiB

Open AccessArticle

Fractional Stochastic Evolution Inclusions with Control on the Boundary

by Hamdy M. Ahmed, Mahmoud M. El-Borai, Wagdy G. El-Sayed and Alaa Y. Elbadrawi

Symmetry 2023, 15(4), 928; https://doi.org/10.3390/sym15040928 - 17 Apr 2023

Cited by 4 | Viewed by 1386

Abstract

Symmetry in systems arises as a result of natural design and provides a pivotal mechanism for crucial system properties. In the field of control theory, scattered research has been carried out concerning the control of group-theoretic symmetric systems. In this manuscript, the principles of stochastic analysis, the fixed-point theorem, fractional calculus, and multivalued map theory are implemented to investigate the null boundary controllability (NBC) of stochastic evolution inclusion (SEI) with the Hilfer fractional derivative (HFD) and the Clarke subdifferential. Moreover, an example is depicted to show the effect of the obtained results. Full article

(This article belongs to the Special Issue Stochastic Analysis with Applications and Symmetry)

22 pages, 1649 KiB

Open AccessFeature PaperArticle

Determination of Mutation Rates with Two Symmetric and Asymmetric Mutation Types

by Jewgeni H. Dshalalow, Van Minh Nguyen, Richard R. Sinden and Ryan T. White

Symmetry 2022, 14(8), 1701; https://doi.org/10.3390/sym14081701 - 16 Aug 2022

Viewed by 2284

Abstract

We revisit our earlier paper, with two of the coauthors, in which we proposed an unbiased and consistent estimator

{\hat{μ}}_{n}

for an unknown mutation rate

μ

of microorganisms. Previously, we proved that the associated sequence of estimators

\{{\hat{μ}}_{n}\}

converges [...] Read more.

We revisit our earlier paper, with two of the coauthors, in which we proposed an unbiased and consistent estimator

{\hat{μ}}_{n}

for an unknown mutation rate

μ

of microorganisms. Previously, we proved that the associated sequence of estimators

\{{\hat{μ}}_{n}\}

converges to

μ

almost surely pointwise on a nonextinct set

Ω_{0}

. Here, we show that this sequence converges also in the mean square with respect to conditional probability measure

P_{0} (\cdot) = P (\cdot \cap Ω_{0}) / P (Ω_{0})

and that, with respect to

P_{0},

the estimator is asymptotically unbiased. We further assume that a microorganism can mutate or turn to a different variant of one of the two types. In particular, it can mean that bacteria under attack by a virus or chemical agent are either perishing or surviving, turning them to stronger variant. We propose estimators for their respective types and show that they are a.s. pointwise and

L^{2}

-consistent and asymptotically unbiased with respect to measure

P_{0}

. Full article

(This article belongs to the Special Issue Stochastic Analysis with Applications and Symmetry)

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24 pages, 871 KiB

Open AccessArticle

On the Exiting Patterns of Multivariate Renewal-Reward Processes with an Application to Stochastic Networks

by Ryan T. White

Symmetry 2022, 14(6), 1167; https://doi.org/10.3390/sym14061167 - 6 Jun 2022

Cited by 1 | Viewed by 2245

Abstract

This article is a study of vector-valued renewal-reward processes on

R^{d}

This article is a study of vector-valued renewal-reward processes on

R^{d}

. The jumps of the process are assumed to be independent and identically distributed nonnegative random vectors with mutually dependent components, each of which may be either discrete or continuous (or a mixture of discrete and continuous components). Each component of the process has a fixed threshold. Operational calculus techniques and symmetries with respect to permutations are used to find a general result for the probability of an arbitrary weak ordering of threshold crossings. The analytic and numerical tractability of the result are demonstrated by an application to the reliability of stochastic networks and some other special cases. Results are shown to agree with empirical probabilities generated through simulation of the process. Full article

(This article belongs to the Special Issue Stochastic Analysis with Applications and Symmetry)

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35 pages, 605 KiB

Open AccessFeature PaperArticle

Skorokhod Reflection Problem for Delayed Brownian Motion with Applications to Fractional Queues

by Giacomo Ascione, Nikolai Leonenko and Enrica Pirozzi

Symmetry 2022, 14(3), 615; https://doi.org/10.3390/sym14030615 - 19 Mar 2022

Cited by 4 | Viewed by 2268

Abstract

Several queueing systems in heavy traffic regimes are shown to admit a diffusive approximation in terms of the Reflected Brownian Motion. The latter is defined by solving the Skorokhod reflection problem on the trajectories of a standard Brownian motion. In recent years, fractional queueing systems have been introduced to model a class of queueing systems with heavy-tailed interarrival and service times. In this paper, we consider a subdiffusive approximation for such processes in the heavy traffic regime. To do this, we introduce the Delayed Reflected Brownian Motion by either solving the Skorohod reflection problem on the trajectories of the delayed Brownian motion or by composing the Reflected Brownian Motion with an inverse stable subordinator. The heavy traffic limit is achieved via the continuous mapping theorem. As a further interesting consequence, we obtain a simulation algorithm for the Delayed Reflected Brownian Motion via a continuous-time random walk approximation. Full article

(This article belongs to the Special Issue Stochastic Analysis with Applications and Symmetry)

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35 pages, 5781 KiB

Open AccessArticle

Asymmetric Density for Risk Claim-Size Data: Prediction and Bimodal Data Applications

by Mansour Shrahili, Ibrahim Elbatal and Haitham M. Yousof

Symmetry 2021, 13(12), 2357; https://doi.org/10.3390/sym13122357 - 7 Dec 2021

Cited by 18 | Viewed by 2160

Abstract

A new, flexible claim-size Chen density is derived for modeling asymmetric data (negative and positive) with different types of kurtosis (leptokurtic, mesokurtic and platykurtic). The new function is used for modeling bimodal asymmetric medical data, water resource bimodal asymmetric data and asymmetric negatively skewed insurance-claims payment triangle data. The new density accommodates the “symmetric”, “unimodal right skewed”, “unimodal left skewed”, “bimodal right skewed” and “bimodal left skewed” densities. The new hazard function can be “decreasing–constant–increasing (bathtub)”, “monotonically increasing”, “upside down constant–increasing”, “monotonically decreasing”, “J shape” and “upside down”. Four risk indicators are analyzed under insurance-claims payment triangle data using the proposed distribution. Since the insurance-claims data are a quarterly time series, we analyzed them using the autoregressive regression model AR(1). Future insurance-claims forecasting is very important for insurance companies to avoid uncertainty about big losses that may be produced from future claims. Full article

(This article belongs to the Special Issue Stochastic Analysis with Applications and Symmetry)

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