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 January 2026 | Viewed by 616

Special Issue Editors


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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

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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Analysis of Stochastic Differential Equations with Applications in Financial Mathematics and Molecular Dynamics, Unpublished PhD Thesis, University of the Aegean, Greece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

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Keywords

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

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Published Papers (1 paper)

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Research

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
Viewed by 381
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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