Special Issue "Stochastic Models with Applications"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics Theory".

Deadline for manuscript submissions: closed (31 December 2021).

Special Issue Editor

Prof. Dr. Antonio Di Crescenzo
E-Mail Website
Guest Editor
Department of Mathematics, University of Salerno, I-84100 Salerno, Italy
Interests: stochastic processes; applied probability; probability theory; stochastic models
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

You are kindly invited to contribute to this Special Issue on “Stochastic Models with Applications” with an original research article or comprehensive review. The focus is mainly on theoretical results and applications of stochastic models aiming to describe systems subject to random perturbations. Stochastic models are ubiquitous in science today, but sometimes they are built under strong assumptions that may limit their use in applications. Here, novel models based on non-classical assumptions are especially appreciated. We look for research based on rigorous mathematical approaches and algorithmic, statistical, and computational methods, with a view to applications related to complex systems and challenging research areas (such as biology and medicine, computer science, economics and finance, epidemiology, information theory, queuing, reliability, statistical physics, and theoretical neurobiology).

Prof. Dr. Antonio Di Crescenzo
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 papers will be 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. Mathematics is an international peer-reviewed open access semimonthly 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 1800 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

  • Complex systems
  • Dependence and copula models
  • Reliability models
  • Random evolution models
  • Markov and semi-Markov models
  • Neural models

Published Papers (12 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

Article
A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions
Mathematics 2021, 9(20), 2605; https://doi.org/10.3390/math9202605 - 16 Oct 2021
Viewed by 365
Abstract
In this paper, we complement a study recently conducted in a paper of H.A. Mombeni, B. Masouri and M.R. Akhoond by introducing five new asymmetric kernel c.d.f. estimators on the half-line [0,), namely the Gamma, inverse Gamma, LogNormal, [...] Read more.
In this paper, we complement a study recently conducted in a paper of H.A. Mombeni, B. Masouri and M.R. Akhoond by introducing five new asymmetric kernel c.d.f. estimators on the half-line [0,), namely the Gamma, inverse Gamma, LogNormal, inverse Gaussian and reciprocal inverse Gaussian kernel c.d.f. estimators. For these five new estimators, we prove the asymptotic normality and we find asymptotic expressions for the following quantities: bias, variance, mean squared error and mean integrated squared error. A numerical study then compares the performance of the five new c.d.f. estimators against traditional methods and the Birnbaum–Saunders and Weibull kernel c.d.f. estimators from Mombeni, Masouri and Akhoond. By using the same experimental design, we show that the LogNormal and Birnbaum–Saunders kernel c.d.f. estimators perform the best overall, while the other asymmetric kernel estimators are sometimes better but always at least competitive against the boundary kernel method from C. Tenreiro. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Show Figures

Figure 1

Article
Time-Inhomogeneous Feller-Type Diffusion Process in Population Dynamics
Mathematics 2021, 9(16), 1879; https://doi.org/10.3390/math9161879 - 07 Aug 2021
Cited by 1 | Viewed by 485
Abstract
The time-inhomogeneous Feller-type diffusion process, having infinitesimal drift α(t)x+β(t) and infinitesimal variance 2r(t)x, with a zero-flux condition in the zero-state, is considered. This process is obtained as a [...] Read more.
The time-inhomogeneous Feller-type diffusion process, having infinitesimal drift α(t)x+β(t) and infinitesimal variance 2r(t)x, with a zero-flux condition in the zero-state, is considered. This process is obtained as a continuous approximation of a birth-death process with immigration. The transition probability density function and the related conditional moments, with their asymptotic behaviors, are determined. Special attention is paid to the cases in which the intensity functions α(t), β(t), r(t) exhibit some kind of periodicity due to seasonal immigration, regular environmental cycles or random fluctuations. Various numerical computations are performed to illustrate the role played by the periodic functions. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Show Figures

Figure 1

Article
Stochastic Comparisons of Some Distances between Random Variables
Mathematics 2021, 9(9), 981; https://doi.org/10.3390/math9090981 - 27 Apr 2021
Cited by 1 | Viewed by 521
Abstract
The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann [...] Read more.
The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Show Figures

Figure 1

Article
On the Cumulants of the First Passage Time of the Inhomogeneous Geometric Brownian Motion
Mathematics 2021, 9(9), 956; https://doi.org/10.3390/math9090956 - 25 Apr 2021
Viewed by 473
Abstract
We consider the problem of the first passage time T of an inhomogeneous geometric Brownian motion through a constant threshold, for which only limited results are available in the literature. In the case of a strong positive drift, we get an approximation of [...] Read more.
We consider the problem of the first passage time T of an inhomogeneous geometric Brownian motion through a constant threshold, for which only limited results are available in the literature. In the case of a strong positive drift, we get an approximation of the cumulants of T of any order using the algebra of formal power series applied to an asymptotic expansion of its Laplace transform. The interest in the cumulants is due to their connection with moments and the accounting of some statistical properties of the density of T like skewness and kurtosis. Some case studies coming from neuronal modeling with reversal potential and mean reversion models of financial markets show the goodness of the approximation of the first moment of T. However hints on the evaluation of higher order moments are also given, together with considerations on the numerical performance of the method. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Show Figures

Figure 1

Article
A Reliability Growth Process Model with Time-Varying Covariates and Its Application
Mathematics 2021, 9(8), 905; https://doi.org/10.3390/math9080905 - 19 Apr 2021
Viewed by 576
Abstract
The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of [...] Read more.
The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of the product under different operational environments. In this paper we introduce an AMSAA-based model considering the covariate effects to measure the influence of the time-varying environmental condition. The parameter estimation of the model is typically performed using maximum likelihood on the failure data. The statistical properties of the estimation in the model are comprehensively derived by the martingale theory. Further inferences including confidence interval estimation and hypothesis tests are designed for the model. The performance and properties of the method are verified in a simulation study, compared with the classical AMSAA model. A case study is used to illustrate the practical use of the model. The proposed approach can be adapted for a wide class of nonhomogeneous Poisson process based models. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Show Figures

Figure 1

Article
On the Increasing Convex Order of Relative Spacings of Order Statistics
Mathematics 2021, 9(6), 618; https://doi.org/10.3390/math9060618 - 15 Mar 2021
Cited by 1 | Viewed by 502
Abstract
Relative spacings are relative differences between order statistics. In this context, we extend previous results concerning the increasing convex order of relative spacings of two distributions from the case of consecutive spacings to general spacings. The sufficient conditions are given in terms of [...] Read more.
Relative spacings are relative differences between order statistics. In this context, we extend previous results concerning the increasing convex order of relative spacings of two distributions from the case of consecutive spacings to general spacings. The sufficient conditions are given in terms of the expected proportional shortfall order. As an application, we compare relative deprivation within some parametric families of income distributions. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Article
Directional Stochastic Orders with an Application to Financial Mathematics
Mathematics 2021, 9(4), 380; https://doi.org/10.3390/math9040380 - 14 Feb 2021
Viewed by 497
Abstract
Relevant integral stochastic orders share a common mathematical model, they are defined by generators which are made up of increasing functions on appropriate directions. Motivated by the aim to provide a unified study of those orders, we introduce a new class of integral [...] Read more.
Relevant integral stochastic orders share a common mathematical model, they are defined by generators which are made up of increasing functions on appropriate directions. Motivated by the aim to provide a unified study of those orders, we introduce a new class of integral stochastic orders whose generators are composed of functions that are increasing on the directions of a finite number of vectors. These orders will be called directional stochastic orders. Such stochastic orders are studied in depth. In that analysis, the conical combinations of vectors in those finite subsets play a relevant role. It is proved that directional stochastic orders are generated by non-stochastic pre-orders and the class of their preserving mappings. Geometrical characterizations of directional stochastic orders are developed. Those characterizations depend on the existence of non-trivial subspaces contained in the set of conical combinations. An application of directional stochastic orders to the field of financial mathematics is developed, namely, to the comparison of investments with random cash flows. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Article
A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve
Mathematics 2021, 9(3), 228; https://doi.org/10.3390/math9030228 - 25 Jan 2021
Cited by 5 | Viewed by 1093
Abstract
The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an [...] Read more.
The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an intensity function based on the Gompertz curve. We discuss the prior distribution of the parameter and we generate samples from the posterior distribution by using Markov Chain Monte Carlo (MCMC) methods. Finally, we illustrate our method analyzing real data associated with COVID-19 in a specific region located at the south of Spain. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Show Figures

Figure 1

Article
Fast Two-Stage Computation of an Index Policy for Multi-Armed Bandits with Setup Delays
Mathematics 2021, 9(1), 52; https://doi.org/10.3390/math9010052 - 29 Dec 2020
Viewed by 574
Abstract
We consider the multi-armed bandit problem with penalties for switching that include setup delays and costs, extending the former results of the author for the special case with no switching delays. A priority index for projects with setup delays that characterizes, in part, [...] Read more.
We consider the multi-armed bandit problem with penalties for switching that include setup delays and costs, extending the former results of the author for the special case with no switching delays. A priority index for projects with setup delays that characterizes, in part, optimal policies was introduced by Asawa and Teneketzis in 1996, yet without giving a means of computing it. We present a fast two-stage index computing method, which computes the continuation index (which applies when the project has been set up) in a first stage and certain extra quantities with cubic (arithmetic-operation) complexity in the number of project states and then computes the switching index (which applies when the project is not set up), in a second stage, with quadratic complexity. The approach is based on new methodological advances on restless bandit indexation, which are introduced and deployed herein, being motivated by the limitations of previous results, exploiting the fact that the aforementioned index is the Whittle index of the project in its restless reformulation. A numerical study demonstrates substantial runtime speed-ups of the new two-stage index algorithm versus a general one-stage Whittle index algorithm. The study further gives evidence that, in a multi-project setting, the index policy is consistently nearly optimal. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Show Figures

Figure 1

Article
On the Size of Subclasses of Quasi-Copulas and Their Dedekind–MacNeille Completion
Mathematics 2020, 8(12), 2238; https://doi.org/10.3390/math8122238 - 18 Dec 2020
Cited by 1 | Viewed by 646
Abstract
We study some topological properties of the class of supermodular n-quasi-copulas and check that the topological size of the Dedekind–MacNeille completion of the set of n-copulas is small, in terms of the Baire category, in the Dedekind–MacNeille completion of the set [...] Read more.
We study some topological properties of the class of supermodular n-quasi-copulas and check that the topological size of the Dedekind–MacNeille completion of the set of n-copulas is small, in terms of the Baire category, in the Dedekind–MacNeille completion of the set of the supermodular n-quasi-copulas, and in turn, this set and the set of n-copulas are small in the set of n-quasi-copulas. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Article
On the Construction of Some Deterministic and Stochastic Non-Local SIR Models
Mathematics 2020, 8(12), 2103; https://doi.org/10.3390/math8122103 - 24 Nov 2020
Cited by 2 | Viewed by 622
Abstract
Fractional-order epidemic models have become widely studied in the literature. Here, we consider the generalization of a simple SIR model in the context of generalized fractional calculus and we study the main features of such model. Moreover, we construct semi-Markov stochastic [...] Read more.
Fractional-order epidemic models have become widely studied in the literature. Here, we consider the generalization of a simple SIR model in the context of generalized fractional calculus and we study the main features of such model. Moreover, we construct semi-Markov stochastic epidemic models by using time changed continuous time Markov chains, where the parent process is the stochastic analog of a simple SIR epidemic. In particular, we show that, differently from what happens in the classic case, the deterministic model does not coincide with the large population limit of the stochastic one. This loss of fluid limit is then stressed in terms of numerical examples. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Show Figures

Figure 1

Article
Copula Modelling on the Dynamic Dependence Structure of Multiple Air Pollutant Variables
Mathematics 2020, 8(11), 1910; https://doi.org/10.3390/math8111910 - 31 Oct 2020
Cited by 8 | Viewed by 689
Abstract
A correlation analysis of pollutant variables provides comprehensive information on dependency behaviour and is thus useful in relating the risk and consequences of pollution events. However, common correlation measurements fail to capture the various properties of air pollution data, such as their non-normal [...] Read more.
A correlation analysis of pollutant variables provides comprehensive information on dependency behaviour and is thus useful in relating the risk and consequences of pollution events. However, common correlation measurements fail to capture the various properties of air pollution data, such as their non-normal distribution, heavy tails, and dynamic changes over time. Hence, they cannot generate highly accurate information. To overcome this issue, this study proposes a combination of the Generalized Autoregressive Conditional Heteroskedasticity model, Generalized Pareto distribution, and stochastic copulas as a tool to investigate the dependence structure between the PM10 variable and other pollutant variables, including CO, NO2, O3, and SO2. Results indicate that the dynamic dependence structure between PM10 and other pollutant variables can be described with a ranking of PM10–CO > PM10–SO2 > PM10–NO2 > PM10–O3 for the overall time paths (δ) and the upper tail (τU) or lower tail (τL) dependency measures. This study reveals an evident correlation among pollutant variables that changes over time; such correlation reflects dynamic dependency. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Show Figures

Figure 1

Back to TopTop