Advances in Stochastic Differential Equations: Theory, Computation and Applications

Dear Colleagues,

Stochastic processes and differential equations are foundational to modeling systems that evolve under uncertainty. Their applications span finance, physics, biology, engineering, and data science, where randomness plays a crucial role in system dynamics. The theoretical landscape has evolved rapidly, incorporating tools like rough path theory, Malliavin calculus, and regularity structures to analyze irregular systems and singular noise.

On the computational side, recent progress in high-order numerical methods, multi-scale solvers, and machine learning-driven inference has enabled simulations of previously intractable models. These innovations have pushed the boundaries of what can be solved both analytically and numerically. Consequently, there is growing synergy between deep theory, algorithmic advances, and practical modeling in domains such as financial markets, neural dynamics, epidemiology, and climate science.

This Special Issue invites original contributions at the intersection of stochastic modeling, differential equations, and their applications. Our aim is to showcase recent theoretical results, innovative numerical methods, and real-world applications that leverage stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs).

We particularly welcome papers that connect rigorous mathematical frameworks with practical relevance, bridging gaps between analysis, computation, and application. The scope of this Special Issue aligns with the journal’s mission to promote interdisciplinary research grounded in advanced mathematical modeling, with special attention being given to problems where uncertainty and randomness are intrinsic features.

Submissions may focus on new theoretical developments, computational techniques, or applied problems where stochastic modeling plays a central role. Reviews or tutorials that survey emerging trends in the field will also be considered.

The aim of this Special Issue is to collect original and high-quality research and review articles related to the development, trends, and challenges in relation to stochastic processes and their applications.

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

• Theoretical analysis of SDEs and SPDEs (existence, uniqueness, and regularity);
• Models with fractional, Lévy, or rough noise;
• Stochastic control, filtering, and inference;
• Malliavin calculus and sensitivity analysis;
• Numerical methods for stochastic systems;
• Uncertainty quantification and stochastic inverse problems;
• Data-driven or machine learning approaches to SDEs;
• Applications in finance, biology, physics, and engineering.

I look forward to receiving your contributions.

Dr. Mustafa Avci
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. Axioms is an international peer-reviewed open access monthly 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 2400 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 (partial) differential equations
• Malliavin and rough-path calculus
• numerical and high-order methods
• uncertainty quantification
• Lévy/jump processes
• machine learning for SDEs
• stochastic control and filtering
• SPDE applications