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 1773

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Department of Mathematics, University of Salerno, I-84100 Salerno, Italy
Interests: stochastic processes; applied probability; probability theory; stochastic models
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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

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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 138
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 765
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>22α1, 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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