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Mathematics
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Stochastic Differential Equations and Applications
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Stochastic Differential Equations and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".

Deadline for manuscript submissions: 30 June 2026 | Viewed by 2282

Special Issue Editors

Dr. Ioannis S. Stamatiou

E-Mail Website
Guest Editor
Department of Surveying and Geoinformatics Engineering, University of West Attica, 12243 Athens, Greece
Interests: stochastic differential equations; numerical methods for stochastic differential equations; mathematical finance; statistical distributions
Prof. Dr. Christos P. Kitsos

E-Mail Website
Guest Editor
School of Engineering, University of West Attica, 12243 Egaleo, Greece
Interests: theoretical and applied statistics; optimal non-linear experimental design; enzyme kinetics; stochastic models; numerical methods; prediction; calibration; information theory-entropy; γ-order probability distributions; invariance; affine geometry in statistics

Special Issue Information

Dear Colleagues,

The Guest Editors welcome papers on stochastic differential equations either with one variable or more which describe an application either for physical sciences or from economics (for example, Brownian motion problems or stock-price problems). The theoretical developments of such problems either from analysis, numerical analysis, or even from stochastic processes are very welcome. The problems in analysis considering Ito–Stratonovic integrals or the investigation of the probability distribution function of the solution process will be appreciated.

In principle, applications can cover probability and mathematics; in addition, we would appreciate an algorithm describing solutions rather than the existence of the solution.

It is our pleasure to invite authors to contribute to this Special Issue by submitting research articles that will be subject to rigorous peer review, aiming to contribute to the development of relevant research in this field.

References:

  1. Halidias and I.S. Stamatiou (2026)-Stochastic Analysis: Financial Mathematics with Matlab , De Gruyter
  2. Kitsos (accepted 2023) - Generalizing the Heat Equation, REVSTAT-Statistical Journal
  3. Kitsos and I.S. Stamatiou (2025) - The γ-order generalized chi-square distribution, Research in Mathematics
  4. I.S. Stamatiou (2016)-Numerical Analysis of Stochastic Differential Equations with Applications in Financial Mathematics and Molecular Dynamics, Unpublished PhD Thesis, University of the Aegean, Greece

Dr. Ioannis S. Stamatiou
Prof. Dr. Christos P. Kitsos
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 250 words) can be sent to the Editorial Office for assessment.

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

  • stochastic differential equations
  • numerical methods for stochastic differential equations
  • stochastic processes
  • mathematical finance

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Published Papers (3 papers)

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Research

29 pages, 665 KB  
Article
Finite-Series Solutions of Hybrid PDE Systems for Conditional Moments of Regime-Switching Extended CEV Processes with Applications in Finance
by Parun Juntanon, Sanae Rujivan and Boualem Djehiche
Mathematics 2026, 14(5), 821; https://doi.org/10.3390/math14050821 - 28 Feb 2026
Viewed by 392
Abstract
This paper develops finite-series solutions of a hybrid system of interconnected partial differential equations for computing the conditional moments of regime-switching extended constant elasticity of variance processes with generalized drift and diffusion coefficients. The regime-switching mechanism is modeled by a continuous-time, finite-state, irreducible [...] Read more.
This paper develops finite-series solutions of a hybrid system of interconnected partial differential equations for computing the conditional moments of regime-switching extended constant elasticity of variance processes with generalized drift and diffusion coefficients. The regime-switching mechanism is modeled by a continuous-time, finite-state, irreducible Markov chain with m regimes, for any integer m≥1. For any real γ>0, we identify a tractable class of processes where the γth conditional moment admits an explicit finite power series representation in the initial state, arising from the polynomial structure. The analytical framework is derived via a Feynman–Kac representation adapted for regime-switching diffusions and validated for accuracy and efficiency using Monte Carlo simulations. In addition, we investigate the asymptotic behavior of the first conditional moment for a two-state regime-switching constant elasticity of variance process with nonlinear drift, emphasizing the effects of symmetry in the Markov intensity matrix and comparisons with the corresponding linear-drift case. Applications in futures pricing demonstrate the framework’s relevance for derivative pricing and risk management. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Applications)
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20 pages, 3806 KB  
Article
An η-Power Stochastic Log-Logistic Diffusion Process: Statistical Computation and Application to Individuals Using the Internet in the United States
by Safa’ Alsheyab
Mathematics 2026, 14(3), 406; https://doi.org/10.3390/math14030406 - 23 Jan 2026
Viewed by 519
Abstract
A new family of stochastic η-power log-logistic diffusion processes was introduced and defined based on the classical log-logistic diffusion model. The probabilistic characteristics of the proposed process were derived through an analysis of the associated stochastic differential equation (SDE), including its explicit [...] Read more.
A new family of stochastic η-power log-logistic diffusion processes was introduced and defined based on the classical log-logistic diffusion model. The probabilistic characteristics of the proposed process were derived through an analysis of the associated stochastic differential equation (SDE), including its explicit expressions, the transition probability density function, and the conditional and non-conditional mean functions. The statistical inference of the model was studied, and parameter estimation was performed using the maximum likelihood method based on discrete sampling paths. The proposed probabilistic and statistical framework was applied to data on individuals using the Internet in the United States to assess the practical performance of the model. The empirical results demonstrated that the inclusion of a power in the process improved the goodness of fit compared with the classical formulation, providing better agreement with the observed data. Finally, a small Monte Carlo experiment was performed to examine the robustness of the estimation procedure. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Applications)
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18 pages, 1681 KB  
Article
Modeling Dynamic Regime Shifts in Diffusion Processes: Approximate Maximum Likelihood Estimation for Two-Threshold Ornstein–Uhlenbeck Models
by Svajone Bekesiene, Anatolii Nikitin and Serhii Nechyporuk
Mathematics 2025, 13(21), 3450; https://doi.org/10.3390/math13213450 - 29 Oct 2025
Cited by 1 | Viewed by 858
Abstract
This study addresses the problem of estimating parameters in a two-threshold Ornstein–Uhlenbeck diffusion process, a model suitable for describing systems that exhibit changes in dynamics when crossing specific boundaries. Such behavior is often observed in real economic and physical processes. The main objective [...] Read more.
This study addresses the problem of estimating parameters in a two-threshold Ornstein–Uhlenbeck diffusion process, a model suitable for describing systems that exhibit changes in dynamics when crossing specific boundaries. Such behavior is often observed in real economic and physical processes. The main objective is to develop and evaluate a method for accurately identifying key parameters, including the threshold levels, drift changes, and diffusion coefficient, within this stochastic framework. The paper proposes an iterative algorithm based on approximate maximum likelihood estimation, which recalculates parameter values step by step until convergence is achieved. This procedure simultaneously estimates both the threshold positions and the associated process parameters, allowing it to adapt effectively to structural changes in the data. Unlike previously studied single-threshold systems, two-threshold models are more natural and offer improved applicability. The method is implemented through custom programming and tested using synthetically generated data to assess its precision and reliability. The novelty of this study lies in extending the approximate maximum likelihood framework to a two-threshold Ornstein–Uhlenbeck process and in developing an iterative estimation procedure capable of jointly recovering both threshold locations and regime-specific parameters with proven convergence properties. Results show that the algorithm successfully captures changes in the process dynamics and provides consistent parameter estimates across different scenarios. The proposed approach offers a practical tool for analyzing systems influenced by shifting regimes and contributes to a better understanding of dynamic processes in various applied fields. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Applications)
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