Advances in Stochastic Differential Equations: Theory, Approximations, and Applications

Dear Colleagues,

Stochastic differential equations (SDEs) constitute a fundamental mathematical framework for modeling dynamical systems subject to random perturbations, with applications ranging from highly volatile financial markets to turbulent fluid flows and contemporary artificial intelligence architectures. Current Special Issue efforts increasingly focus on narrowing the discrepancy between idealized theoretical formulations and complex real-world phenomena, leveraging advanced approximation methodologies and machine learning techniques to transform abstract SDE-based models into robust, computationally efficient tools with significant practical impact.

Topics of interest include, but are not limited to, the following:

- Theoretical developments arising from recent advances in the analysis of stochastic differential equations, particularly those involving the incorporation of driving processes that extend beyond classical Brownian motion. Notable examples include Lévy jump processes, fractional or partial Brownian motions, and symmetric α-stable processes, which together provide a more flexible framework for modeling complex, highly irregular phenomena observed in applications such as quantitative finance and statistical physics.

- Numerically robust approximation techniques and computational methods for nonlinear stochastic differential equations (SDEs), encompassing both classical discretization schemes—such as the Euler–Maruyama and Milstein methods—and contemporary high‑order strategies, including path‑wise decomposition approaches, adaptive step‑size algorithms, Wong–Zakai-type regularization procedures, and related variants, which collectively yield accelerated convergence rates for both strong and weak solutions while enhancing numerical stability.

- Real-world impact of stochastic differential equation theory: advancing quantitative finance, engineering and physics, biological sciences and medicine, artificial intelligence, control theory, and related areas.

- Comprehensive review studies that synthesize and critically evaluate the role and impact of stochastic differential equations in advancing theoretical research and practical applications within the corresponding disciplinary domain.

Prof. Dr. Petras Rupšys
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 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-anonymized 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.

• stochastic differential equations
• data science
• variable structure control theory
• complex theory
• complex network theory
• stochastic modeling for artificial intelligence and machine learning
• biological regulation
• fuzzy differential equations, and modeling
• statistical inference
• probability theory