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Mathematics
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Applied Probability, Statistics and Operational Research
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Applied Probability, Statistics and Operational Research

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: closed (30 June 2025) | Viewed by 1655

Special Issue Editors

Dr. Tiandong Wang

E-Mail Website
Guest Editor
Shanghai Center for Mathematical Sciences, Fudan University, 2005 Songhu Rd., Shanghai 200433, China
Interests: the interface of applied probability and statistics, especially the modeling of heavy-tailed phenomena in complex networks
Dr. Lizhen Lin

E-Mail Website
Guest Editor
Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA
Interests: Bayesian asymptotics; Bayesian nonparametrics; big data analysis; geometry and statistics; network analysis; probabilistic graphical models; topological data analysis
Dr. Zifeng Zhao

E-Mail Website
Guest Editor
Department of Information Technology, Analytics, and Operations, Mendoza College of Business, University of Notre Dame, Notre Dame, IN 46556, USA
Interests: financial risk management; portfolio optimization; insurance risk classification and pricing, and web search traffic forecasting

Special Issue Information

Dear Colleagues,

In the era of big data, a significant amount of research efforts has been devoted to the inter-discipline of applied probability, statistics, and operations research, with new methodologies and theories developed to resolve real-life problems. The focus of this Special Issue is oriented toward, but not limited to, the asymptotic analysis and optimization of probabilistic models, the development of novel statistical inference methods, as well as the data-driven decision-making process. Applications of new analytical tools to interesting real-life scenarios are also welcome. This Special Issue aims to provide a platform for researchers in the three disciplines to share their recent advances related to the fields and discuss insights into future research opportunities and challenges.

Dr. Tiandong Wang
Dr. Lizhen Lin
Dr. Zifeng Zhao
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. 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 2600 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

  • applied probability
  • statistical inference
  • stochastic processes and applications
  • stochastic control
  • optimization
  • statistical learning
  • fuzzy methods

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Published Papers (2 papers)

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19 pages, 408 KB  
Article
On the Critical Parameters of Branching Random Walks
by Daniela Bertacchi and Fabio Zucca
Mathematics 2025, 13(18), 2962; https://doi.org/10.3390/math13182962 - 12 Sep 2025
Viewed by 74
Abstract
Given a discrete spatial structure X, we define continuous-time branching processes {ηt}t≥0 that model a population breeding and dying on X. These processes are usually called branching random walks, and ηt(x) [...] Read more.
Given a discrete spatial structure X, we define continuous-time branching processes {ηt}t≥0 that model a population breeding and dying on X. These processes are usually called branching random walks, and ηt(x) denotes the number of individuals alive at site x at time t. They are characterised by breeding rates kxy (governing the rate at which individuals at x send offspring to y) and by a multiplicative speed parameter λ. These processes also serve as models for epidemic spreading, where λkxy represents the infection rate from x to y. In this context, ηt(x) represents the number of infected individuals at x at time t, and the removal of an individual is due to either death or recovery. Two critical parameters of interest are the global critical parameter λw, related to global survival, and the local critical parameter λs, related to survival within finite sets (with λw≤λs). In disease or pest control, the primary goal is to lower λ so that the process dies out, at least locally. Nevertheless, a process that survives globally can still pose a threat, especially if sudden changes cause global survival to transition into local survival. In fact, local modifications to the rates can affect the values of both critical parameters, making it important to understand when and how they can be increased. Using results on the comparison of the extinction probabilities for a single branching random walk across different sets, we extend the analysis to the extinction probabilities and critical parameters of pairs of branching random walks whose rates coincide outside a fixed set A⊆X. We say that two branching random walks are equivalent if their rates coincide everywhere except on a finite subset of X. Given an equivalence class of branching random walks, we prove that if one process has λw*≠λs*, then λw* is the maximal possible value of this parameter within the class. We describe the possible configurations for the critical parameters within these equivalence classes. Full article
(This article belongs to the Special Issue Applied Probability, Statistics and Operational Research)
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22 pages, 1975 KB  
Article
A Majority Theorem for the Uncapacitated p = 2 Median Problem and Local Spatial Autocorrelation
by Daniel A. Griffith, Yongwan Chun and Hyun Kim
Mathematics 2025, 13(2), 249; https://doi.org/10.3390/math13020249 - 13 Jan 2025
Cited by 1 | Viewed by 915
Abstract
The existing quantitative geography literature contains a dearth of articles that span spatial autocorrelation (SA), a fundamental property of georeferenced data, and spatial optimization, a popular form of geographic analysis. The well-known location–allocation problem illustrates this state of affairs, although its empirical geographic [...] Read more.
The existing quantitative geography literature contains a dearth of articles that span spatial autocorrelation (SA), a fundamental property of georeferenced data, and spatial optimization, a popular form of geographic analysis. The well-known location–allocation problem illustrates this state of affairs, although its empirical geographic distribution of demand virtually always exhibits positive SA. This latent redundant attribute information alludes to other tools that may well help to solve such spatial optimization problems in an improved, if not better than, heuristic way. Within a proof-of-concept perspective, this paper articulates connections between extensions of the renowned Majority Theorem of the minisum problem and especially the local indices of SA (LISA). The relationship articulation outlined here extends to the p = 2 setting linkages already established for the p = 1 spatial median problem. In addition, this paper presents the foundation for a novel extremely efficient p = 2 algorithm whose formulation demonstratively exploits spatial autocorrelation. Full article
(This article belongs to the Special Issue Applied Probability, Statistics and Operational Research)
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