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Axioms
Special Issues
Stochastic Modeling and Its Analysis
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Stochastic Modeling and Its Analysis

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

Deadline for manuscript submissions: closed (28 February 2025) | Viewed by 4259

Special Issue Editors

Prof. Dr. Chao Liu

E-Mail Website
Guest Editor
Insitute of Systems Science, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Interests: stochastic process; modeling and dynamical analyses of biological systems and infectious systems; computer simulation
Dr. Qun Liu

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
Interests: stochastic differential equations and their applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to publish original research articles covering advances in the theory of stochastic modeling in phenomena arising from the real world. In this framework, stochastic continuous and discrete time processes will be discussed, as will stochastic optimal controls and computer simulation techniques. All of the above topics are intended to be treated in the spirit of modeling the evolution of stochastic systems of interest in biology, infectious diseases, economics, and other related research fields.

Potential topics include, but are not limited to, the following:

  • Stochastic processes for economic activity;
  • Stochastic models and analyses for biological systems;
  • Stochastic models and analyses applied to epidemiology;
  • Stochastic computational biology;
  • Stochastic optimal control for biological systems;
  • Parameter estimation and sensitivity analyses of stochastic biological systems. 

Prof. Dr. Chao Liu
Dr. Qun Liu
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

  • stochastic process
  • stochastic persistence in mean
  • ergodicity
  • uniqueness and existence of global positive solutions
  • optimal control

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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

24 pages, 398 KiB  
Article
Objective Posterior Analysis of kth Record Statistics in Gompertz Model
by Zoran Vidović and Liang Wang
Axioms 2025, 14(3), 152; https://doi.org/10.3390/axioms14030152 - 20 Feb 2025
Viewed by 378
Abstract
The Gompertz distribution has proven highly valuable in modeling human mortality rates and assessing the impacts of catastrophic events, such as plagues, financial crashes, and famines. Record data, which capture extreme values and critical trends, are particularly relevant for analyzing such phenomena. In [...] Read more.
The Gompertz distribution has proven highly valuable in modeling human mortality rates and assessing the impacts of catastrophic events, such as plagues, financial crashes, and famines. Record data, which capture extreme values and critical trends, are particularly relevant for analyzing such phenomena. In this study, we propose an objective Bayesian framework for estimating the parameters of the Gompertz distribution using record data. We analyze the performance of several objective priors, including the reference prior, Jeffreys’ prior, the maximal data information (MDI) prior, and probability matching priors. The suitability and properties of the resulting posterior distributions are systematically examined for each prior. A detailed simulation study is performed to assess the effectiveness of various estimators based on the performance criteria. To demonstrate the practical application of the methodology, it is applied to a real-world dataset. This study contributes to the field by providing a thorough comparative evaluation of objective priors and showcasing their impact and applicability in parameter estimation for Gompertz distribution based on record values. Full article
(This article belongs to the Special Issue Stochastic Modeling and Its Analysis)
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18 pages, 446 KiB  
Article
Strong Consistency of Incomplete Functional Percentile Regression
by Mohammed B. Alamari, Fatimah A. Almulhim, Ouahiba Litimein and Boubaker Mechab
Axioms 2024, 13(7), 444; https://doi.org/10.3390/axioms13070444 - 30 Jun 2024
Viewed by 993
Abstract
This paper analyzes the co-fluctuation between a scalar response random variable and a curve regressor using quantile regression. We focus on the situation wherein the output variable is observed with random missing. For this incomplete functional data situation, we estimate the quantile regression [...] Read more.
This paper analyzes the co-fluctuation between a scalar response random variable and a curve regressor using quantile regression. We focus on the situation wherein the output variable is observed with random missing. For this incomplete functional data situation, we estimate the quantile regression by combining two principal nonparametric methods: the local linearity approach (LLA) and the kernel nearest neighbor (KNN) algorithm. We study the asymptotic properties of the constructed estimator by establishing, under general assumptions, uniform consistency over the number of neighborhoods. This asymptotic result provides good mathematical support for the selection of the optimal neighborhood. We examine the feasibility of the constructed estimator using artificially generated data. Moreover, we apply the quantile regression technique in food quality by predicting the riboflavin quantity in yogurt using spectrometry data. Full article
(This article belongs to the Special Issue Stochastic Modeling and Its Analysis)
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31 pages, 401 KiB  
Article
One-Dimensional BSDEs with Jumps and Logarithmic Growth
by El Mountasar Billah Bouhadjar, Nabil Khelfallah and Mhamed Eddahbi
Axioms 2024, 13(6), 354; https://doi.org/10.3390/axioms13060354 - 24 May 2024
Viewed by 902
Abstract
In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic growth in both the state variable and the Brownian component while maintaining Lipschitz continuity with [...] Read more.
In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic growth in both the state variable and the Brownian component while maintaining Lipschitz continuity with respect to the jump component. Our study rigorously establishes the existence and uniqueness of solutions within suitable functional spaces. Additionally, we relax the Lipschitz condition on the Poisson component, permitting the generator to exhibit logarithmic growth with respect to all variables. Taking a step further, we employ an exponential transformation to establish an equivalence between a solution of a BSDEJ exhibiting quadratic growth in the z-variable and a BSDEJ showing a logarithmic growth with respect to y and z. Full article
(This article belongs to the Special Issue Stochastic Modeling and Its Analysis)
25 pages, 399 KiB  
Article
Malliavin Regularity of Non-Markovian Quadratic BSDEs and Their Numerical Schemes
by Salima Doubbakh, Nabil Khelfallah, Mhamed Eddahbi and Anwar Almualim
Axioms 2023, 12(4), 366; https://doi.org/10.3390/axioms12040366 - 10 Apr 2023
Viewed by 1296
Abstract
We study both Malliavin regularity and numerical approximation schemes for a class of quadratic backward stochastic differential equations (QBSDEs for short) in cases where the terminal data need not be a function of a forward diffusion. By using the connection between the QBSDE [...] Read more.
We study both Malliavin regularity and numerical approximation schemes for a class of quadratic backward stochastic differential equations (QBSDEs for short) in cases where the terminal data need not be a function of a forward diffusion. By using the connection between the QBSDE under study and some backward stochastic differential equations (BSDEs) with global Lipschitz coefficients, we firstly prove Lq, (q≥2) existence and uniqueness results for QBSDE. Secondly, the Lp-Hölder continuity of the solutions is established for (q>4 and 2≤p<q2). Then, we analyze some numerical schemes for our systems and establish their rates of convergence. Moreover, our results are illustrated with three examples. Full article
(This article belongs to the Special Issue Stochastic Modeling and Its Analysis)
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