Probability Theory, Statistical Inference and Stochastic Analysis with Applications

Dear Colleagues,

Over recent decades, the interaction between probability, statistics, and stochastic modeling has deepened substantially, motivated by challenges arising in fields such as quantitative finance, signal processing, machine learning, statistical physics, biological systems, and the modeling of uncertainty in high-dimensional or functional data. This Special Issue aims to bring together high-quality contributions at the forefront of modern probability theory, statistical inference, and stochastic analysis, with particular emphasis on methodologies, theoretical developments, and innovative applications driven by complex stochastic systems.

We welcome original research articles that advance the mathematical foundations of probability theory, including convergence principles, limit theorems, concentration inequalities, empirical process theory, stochastic calculus, and random fields. Contributions addressing recent trends in nonparametric and semiparametric inference, robust statistics, high-dimensional inference, Bayesian approaches, and statistical learning theory are particularly encouraged. Work exploring asymptotic properties of estimators, dependence structures, stochastic orders, and the behavior of complex random objects—such as U-statistics, stochastic processes, and functional data—falls well within the scope of this Special Issue.

From the applied perspective, we invite submissions that demonstrate how modern probabilistic and statistical tools can be leveraged to analyze stochastic differential equations (SDEs and SPDEs), time-varying or nonstationary systems, stochastic optimization procedures, random networks, and problems involving uncertainty quantification. Applications to data-driven modeling in engineering, environmental sciences, epidemiology, and emerging domains such as stochastic machine learning algorithms and probabilistic numerics are highly welcome.

By gathering theoretical advances and application-oriented studies under a unified theme, this Special Issue seeks to highlight the vitality of stochastic methods in contemporary science and to foster dialogue between probabilists, statisticians, and practitioners. We particularly encourage interdisciplinary work that showcases how rigorous probabilistic reasoning and statistical methodology can address real-world problems exhibiting uncertainty, complexity, or randomness.

Prof. Dr. Salim Bouzebda
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-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.

• advanced probability theory
• asymptotic analysis
• statistical inference
• complex and high-dimensional settings
• differential systems
• stochastic analysis
• stochastic optimization
• modeling
• uncertainty quantification