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Mathematics
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Stochastic Models with Applications, 2nd Edition
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Stochastic Models with Applications, 2nd Edition

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 1911

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, 2nd Edition” with an original research article or comprehensive review. The focus is mainly on theoretical results and applications of stochastic models with the aim of describing 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 are looking for research based on rigorous mathematical approaches and algorithmic, statistical, and computational methods, with a view toward 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).

This Special Issue is a continuation of the previous successful Special Issue “Stochastic Models with Applications”.

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 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

  • complex systems
  • dependence and copula models
  • reliability models
  • random evolution models
  • Markov and semi-Markov models
  • neural models
  • random walks
  • queueing models
  • stochastic models and Cybersecurity

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Published Papers (2 papers)

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Research

13 pages, 247 KiB  
Article
Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics
by Mariya Svishchuk and Anatoliy V. Swishchuk
Mathematics 2025, 13(9), 1440; https://doi.org/10.3390/math13091440 - 28 Apr 2025
Viewed by 254
Abstract
This paper is devoted to the study of stochastic optimal control of averaged stochastic differential delay equations (SDDEs) with semi-Markov switchings and their applications in economics. By using the Dynkin formula and solution of the Dirichlet–Poisson problem, the Hamilton–Jacobi–Bellman (HJB) equation and the [...] Read more.
This paper is devoted to the study of stochastic optimal control of averaged stochastic differential delay equations (SDDEs) with semi-Markov switchings and their applications in economics. By using the Dynkin formula and solution of the Dirichlet–Poisson problem, the Hamilton–Jacobi–Bellman (HJB) equation and the inverse HJB equation are derived. Applications are given to a new Ramsey stochastic models in economics, namely the averaged Ramsey diffusion model with semi-Markov switchings. A numerical example is presented as well. Full article
(This article belongs to the Special Issue Stochastic Models with Applications, 2nd Edition)
17 pages, 333 KiB  
Article
Stochastic Quasi-Geostrophic Equation with Jump Noise in Lp Spaces
by Jiahui Zhu, Xinyun Wang and Heling Su
Mathematics 2023, 11(22), 4608; https://doi.org/10.3390/math11224608 - 10 Nov 2023
Viewed by 777
Abstract
In this paper, we consider a 2D stochastic quasi-geostrophic equation driven by jump noise in a smooth bounded domain. We prove the local existence and uniqueness of mild Lp(D)-solutions for the dissipative quasi-geostrophic equation with a full range [...] Read more.
In this paper, we consider a 2D stochastic quasi-geostrophic equation driven by jump noise in a smooth bounded domain. We prove the local existence and uniqueness of mild Lp(D)-solutions for the dissipative quasi-geostrophic equation with a full range of subcritical powers α∈(12,1] by using the semigroup theory and fixed point theorem. Our approach, based on the Yosida approximation argument and Itô formula for the Banach space valued processes, allows for establishing some uniform bounds for the mild solutions and we prove the global existence of mild solutions in L∞(0,T;Lp(D)) space for all p>22α−1, which is consistent with the deterministic case. Full article
(This article belongs to the Special Issue Stochastic Models with Applications, 2nd Edition)
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