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Axioms
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Research on Stochastic Analysis and Applied Statistics
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Research on Stochastic Analysis and Applied Statistics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 28 February 2026 | Viewed by 4474

Special Issue Editors

Dr. Shusen Pu

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of West Florida, Pensacola, FL 32514, USA
Interests: data science; applied statistics; computational neuroscience; stochastic processes
Prof. Dr. Subhash Bagui

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of West Florida, Pensacola, FL 32514, USA
Interests: nonparametric classification/discrimination; statistical pattern recognition; cluster analysis; data mining; biostatistics; design, and analysis of experiments; statistical computing and applied statistics

Special Issue Information

Dear Colleagues,

This Special Issue delves into the interplay between stochastic analysis, applied statistics, and the transformative impacts of machine learning and deep learning. With a comprehensive scope that spans mathematical modeling, statistics, and data science, this initiative seeks to bridge the gap between theoretical understanding and practical applications. The issue covers topics such as stochastic processes and applied probability, which are pivotal in various disciplines for modeling unpredictability. It highlights the importance of statistical modeling and data analysis in navigating complex datasets and extracting deep insights, thus showcasing their relevance in fields like healthcare analytics and financial forecasting.

Moreover, the issue emphasizes the role of computational statistics and the algorithmic advancements tailored to address the challenges of handling large volumes of data. These efforts include the development of the advanced statistical software and tools essential for modern data analysis. The fusion of machine learning and deep learning with traditional statistical methods represents a key theme, illustrating how these innovative technologies can improve pattern recognition and predictive modeling in large and complex datasets.

Targeting a wide readership, this Special Issue fosters interdisciplinary dialogue among professionals, academics, and students. It serves as a valuable resource for those interested in the theory behind stochastic processes and the practical application of statistical methods to real-world problems. By showcasing the latest research findings and methodological innovations, this Issue aims to inspire further research and practical applications in the ever-evolving fields of statistics, data science, and mathematical modeling, making a significant contribution to their advancement.

Dr. Shusen Pu
Prof. Dr. Subhash Bagui
Guest Editors

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. Axioms 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

  • statistical modelling
  • applied probability
  • data analysis
  • computational statistics
  • stochastic processes
  • machine learning
  • deep learning

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

11 pages, 243 KiB  
Article
Conditional Exponential Convex Functions on White Noise Spaces
by Ahmed. M. Zabel, Areej A. Almoneef, Ayat Nassar and Abd-Allah Hyder
Axioms 2025, 14(3), 223; https://doi.org/10.3390/axioms14030223 - 18 Mar 2025
Viewed by 186
Abstract
This paper seeks to present the fundamental features of the category of conditional exponential convex functions (CECFs). Additionally, the study of continuous CECFs contributes to the characterization of convolution semigroups. In this context, we expand our focus to include a much broader class [...] Read more.
This paper seeks to present the fundamental features of the category of conditional exponential convex functions (CECFs). Additionally, the study of continuous CECFs contributes to the characterization of convolution semigroups. In this context, we expand our focus to include a much broader class of Gaussian processes, where we define the generalized Fourier transform in a more straightforward manner. This approach is closely connected to the method by which we derived the Gaussian process, utilizing the framework of a Gelfand triple and the theorem of Bochner–Minlos. A part of this work involves constructing the reproducing kernel Hilbert spaces (RKHS) directly from CECFs. Full article
(This article belongs to the Special Issue Research on Stochastic Analysis and Applied Statistics)
19 pages, 10209 KiB  
Article
Exploring Stochastic Heat Equations: A Numerical Analysis with Fast Discrete Fourier Transform Techniques
by Ahmed G. Khattab, Mourad S. Semary, Doaa A. Hammad and Aisha F. Fareed
Axioms 2024, 13(12), 886; https://doi.org/10.3390/axioms13120886 - 21 Dec 2024
Viewed by 725
Abstract
This paper presents an innovative numerical technique for specific classes of stochastic heat equations. Our approach uniquely combines a sixth-order compact finite difference algorithm with fast discrete Fourier transforms. While traditional discrete sine transforms are effective for approximating second-order derivatives, they are inadequate [...] Read more.
This paper presents an innovative numerical technique for specific classes of stochastic heat equations. Our approach uniquely combines a sixth-order compact finite difference algorithm with fast discrete Fourier transforms. While traditional discrete sine transforms are effective for approximating second-order derivatives, they are inadequate for first-order derivatives. To address this limitation, we introduce an innovative variant based on exponential transforms. This method is rigorously evaluated on two forms of stochastic heat equations, and the solutions are compared with those obtained using the established stochastic ten non-polynomial cubic-spline method. The results confirm the accuracy and applicability of our proposed method, highlighting its potential to enhance the numerical treatment of stochastic heat equations. Full article
(This article belongs to the Special Issue Research on Stochastic Analysis and Applied Statistics)
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30 pages, 1419 KiB  
Article
A Theoretical Review of Area Production Rates as Test Statistics for Detecting Nonequilibrium Dynamics in Ornstein–Uhlenbeck Processes
by Alexander Strang
Axioms 2024, 13(12), 820; https://doi.org/10.3390/axioms13120820 - 24 Nov 2024
Viewed by 819
Abstract
A stochastic process is at thermodynamic equilibrium if it obeys time-reversal symmetry; forward and reverse time are statistically indistinguishable at a steady state. Nonequilibrium processes break time-reversal symmetry by maintaining circulating probability currents. In physical processes, these currents require a continual use and [...] Read more.
A stochastic process is at thermodynamic equilibrium if it obeys time-reversal symmetry; forward and reverse time are statistically indistinguishable at a steady state. Nonequilibrium processes break time-reversal symmetry by maintaining circulating probability currents. In physical processes, these currents require a continual use and exchange of energy. Accordingly, signatures of nonequilibrium behavior are important markers of energy use in biophysical systems. In this article, we consider a particular signature of nonequilibrium behavior: area production rates. These are the average rate at which a stochastic process traces out signed area in its projections onto coordinate planes. Area production is an example of a linear observable: a path integral over an observed trajectory against a linear vector field. We provide a summary review of area production rates in Ornstein–Uhlenbeck (OU) processes. Then, we show that, given an OU process, a weighted Frobenius norm of the area production rate matrix is the optimal test statistic for detecting nonequilibrium behavior in the sense that its coefficient of variation decays faster in the length of time observed than the coefficient of variation of any other linear observable. We conclude by showing that this test statistic estimates the entropy production rate of the process. Full article
(This article belongs to the Special Issue Research on Stochastic Analysis and Applied Statistics)
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27 pages, 4691 KiB  
Article
Enhanced Real-Life Data Modeling with the Modified Burr III Odds Ratio–G Distribution
by Haochong Yang, Mingfang Huang, Xinyu Chen, Ziyan He and Shusen Pu
Axioms 2024, 13(6), 401; https://doi.org/10.3390/axioms13060401 - 14 Jun 2024
Cited by 2 | Viewed by 2107
Abstract
In this study, we introduce the modified Burr III Odds Ratio–G distribution, a novel statistical model that integrates the odds ratio concept with the foundational Burr III distribution. The spotlight of our investigation is cast on a key subclass within this innovative framework, [...] Read more.
In this study, we introduce the modified Burr III Odds Ratio–G distribution, a novel statistical model that integrates the odds ratio concept with the foundational Burr III distribution. The spotlight of our investigation is cast on a key subclass within this innovative framework, designated as the Burr III Scaled Inverse Odds Ratio–G (B-SIOR-G) distribution. By effectively integrating the odds ratio with the Burr III distribution, this model enhances both flexibility and predictive accuracy. We delve into a thorough exploration of this distribution family’s mathematical and statistical properties, spanning hazard rate functions, quantile functions, moments, and additional features. Through rigorous simulation, we affirm the robustness of the B-SIOR-G model. The flexibility and practicality of the B-SIOR-G model are demonstrated through its application to four datasets, highlighting its enhanced efficacy over several well-established distributions. Full article
(This article belongs to the Special Issue Research on Stochastic Analysis and Applied Statistics)
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