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Mathematics
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New Advances in Applied Probability and Stochastic Processes
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New Advances in Applied Probability and Stochastic Processes

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

Deadline for manuscript submissions: closed (31 May 2024) | Viewed by 4886

Special Issue Editor

Dr. Damjan Škulj

E-Mail Website
Guest Editor
Faculty of Social Sciences, University of Ljubljana, Kardeljeva pl. 5, SI-1000 Ljubljana, Slovenia
Interests: stochastic processes; Markov chains; imprecise probabilities; numerical optimization; network analysis

Special Issue Information

Dear Colleagues,

For this Special Issue, we seek original, previously unpublished research papers of high quality in the field of applied probability and stochastic processes. Contributions on relevant aspects of current topics in the general theory of probability and stochastic processes are welcome, as are those dealing specifically with the modelling of uncertainty, imprecise probabilities, or fuzzy probabilities. Contributions dealing with the application of the theories of probability and stochastic processes to the solution of real-world problems are particularly welcome.

Submissions must have sufficient mathematical depth, be rigorous and systematic, be clearly presented, and be written in correct English. There are no restrictions on the length of papers or the use of colored figures and diagrams.

Dr. Damjan Škulj
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. 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
  • Markov processes
  • stochastic analysis
  • copulas
  • imprecise probabilities
  • fuzzy probability
  • risk modelling
  • uncertainty
  • reliability
  • numerical methods in probability
  • probabilistic optimization
  • probability in finance

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

Published Papers (4 papers)

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Research

8 pages, 264 KiB  
Article
Relations among the Queue-Length Probabilities in the Pre-Arrival, Random, and Post-Departure Epochs in the GI/Ma,b/c Queue
by Jing Gai and Mohan Chaudhry
Mathematics 2024, 12(17), 2609; https://doi.org/10.3390/math12172609 - 23 Aug 2024
Viewed by 439
Abstract
In this paper, we present research results that extend and supplement our article recently published by MDPI. We derive the closed-form relations among the queue-length probabilities observed in the pre-arrival, random, and post-departure epochs for a complex, bulk-service, multi-server queueing system GI/M [...] Read more.
In this paper, we present research results that extend and supplement our article recently published by MDPI. We derive the closed-form relations among the queue-length probabilities observed in the pre-arrival, random, and post-departure epochs for a complex, bulk-service, multi-server queueing system GI/Ma,b/c. Full article
(This article belongs to the Special Issue New Advances in Applied Probability and Stochastic Processes)
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21 pages, 2247 KiB  
Article
The Lomax-Exponentiated Odds Ratio–G Distribution and Its Applications
by Sudakshina Singha Roy, Hannah Knehr, Declan McGurk, Xinyu Chen, Achraf Cohen and Shusen Pu
Mathematics 2024, 12(10), 1578; https://doi.org/10.3390/math12101578 - 18 May 2024
Cited by 2 | Viewed by 868
Abstract
This paper introduces the Lomax-exponentiated odds ratio–G (L-EOR–G) distribution, a novel framework designed to adeptly navigate the complexities of modern datasets. It blends theoretical rigor with practical application to surpass the limitations of traditional models in capturing complex data attributes such as heavy [...] Read more.
This paper introduces the Lomax-exponentiated odds ratio–G (L-EOR–G) distribution, a novel framework designed to adeptly navigate the complexities of modern datasets. It blends theoretical rigor with practical application to surpass the limitations of traditional models in capturing complex data attributes such as heavy tails, shaped curves, and multimodality. Through a comprehensive examination of its theoretical foundations and empirical data analysis, this study lays down a systematic theoretical framework by detailing its statistical properties and validates the distribution’s efficacy and robustness in parameter estimation via Monte Carlo simulations. Empirical evidence from real-world datasets further demonstrates the distribution’s superior modeling capabilities, supported by compelling various goodness-of-fit tests. The convergence of theoretical precision and practical utility heralds the L-EOR–G distribution as a groundbreaking advancement in statistical modeling, significantly enhancing precision and adaptability. The new model not only addresses a critical need within statistical modeling but also opens avenues for future research, including the development of more sophisticated estimation methods and the adaptation of the model for various data types, thereby promising to refine statistical analysis and interpretation across a wide array of disciplines. Full article
(This article belongs to the Special Issue New Advances in Applied Probability and Stochastic Processes)
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8 pages, 244 KiB  
Article
Green Measures for a Class of Non-Markov Processes
by Herry P. Suryawan and José L. da Silva
Mathematics 2024, 12(9), 1334; https://doi.org/10.3390/math12091334 - 27 Apr 2024
Viewed by 746
Abstract
In this paper, we investigate the Green measure for a class of non-Gaussian processes in Rd. These measures are associated with the family of generalized grey Brownian motions Bβ,α, 0<β≤1, [...] Read more.
In this paper, we investigate the Green measure for a class of non-Gaussian processes in Rd. These measures are associated with the family of generalized grey Brownian motions Bβ,α, 0<β≤1, 0<α≤2. This family includes both fractional Brownian motion, Brownian motion, and other non-Gaussian processes. We show that the perpetual integral exists with probability 1 for dα>2 and 1<α≤2. The Green measure then generalizes those measures of all these classes. Full article
(This article belongs to the Special Issue New Advances in Applied Probability and Stochastic Processes)
18 pages, 4869 KiB  
Article
Geometric Probability Analysis of Meeting Probability and Intersection Duration for Triple Event Concurrency
by Mohammad Al Bataineh, Zouhair Al-qudah, Atef Abdrabou and Ayman N. Sandokah
Mathematics 2023, 11(12), 2708; https://doi.org/10.3390/math11122708 - 15 Jun 2023
Viewed by 2163
Abstract
This study investigates the dynamics of three discrete independent events occurring randomly and repeatedly within the interval [0,T]. Each event spans a predetermined fraction γ of the total interval length T before concluding. Three independent continuous random variables [...] Read more.
This study investigates the dynamics of three discrete independent events occurring randomly and repeatedly within the interval [0,T]. Each event spans a predetermined fraction γ of the total interval length T before concluding. Three independent continuous random variables represent the starting times of these events, uniformly distributed over the time interval [0,T]. By employing a geometric probability approach, we derive a rigorous closed-form expression for the probability of the joint occurrence of these three events, taking into account various values of the fraction γ. Additionally, we determine the expected value of the intersection duration of the three events within the time interval [0,T]. Furthermore, we provide a comprehensive solution for evaluating the expected number of trials required for the simultaneous occurrence of these events. Numerous numerical examples support the theoretical analysis presented in this paper, further validating our findings. Full article
(This article belongs to the Special Issue New Advances in Applied Probability and Stochastic Processes)
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