Numerical Analysis of Stochastic Differential Equations and Their Applications

Dear Colleagues,

Stochastic differential equations have an extensive range of applications, including in engineering, biology, physics, and finance. They are a fundamental stochastic modeling tool for sampling algorithms in machine learning and now in financial theory too. Stochastic differential equations are essential to our understanding of the complex movement of particles in fluids, which is one of the most fascinating aspects of particle physics and quantum mechanics. The underlying dynamics in most of their applications are so complicated that it is impossible to solve stochastic differential equations analytically; therefore, numerical techniques are used to determine their approximate solutions.

This Special Issue on the "Numerical Analysis of Stochastic Differential Equations and Their Applications" aims to publish excellent papers on the use of statistical inference to solve stochastic differential equations and their applications, seeking to promote creativity, vitality, and cross-disciplinary interaction in this area of research. We encourage submissions related to all aspects of stochastic system analysis, stochastic modeling and identification, optimization, filtering, and control, as well as associated issues related to the theory of stochastic differential equations. This Special Issue aims to promote synergy between stochastic differential equation theory and related large-scale computations. The topics listed below, as well as other related topics, are welcome in this Special Issue:

• Trends and challenges related to stochastic differential equations;
• Optimal control problems governed by stochastic differential equations;
• Numerical treatment of stochastic differential equations;
• Multilevel Monte Carlo methods;
• Simulation of stochastic differential equations and parameter estimators;
• Stochastic differential equations driven by Lévy processes;
• Malliavin calculus;
• Modeling and applications in supervised and unsupervised machine learning;
• Linking artificial intelligence with stochastic differential equations.

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 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. 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.

• trends and challenges related to stochastic differential equations
• optimal control problems governed by stochastic differential equations
• numerical treatment of stochastic differential equations
• multilevel Monte Carlo methods
• simulation of stochastic differential equations and parameter estimators
• stochastic differential equations driven by Lévy processes
• malliavin calculus
• modeling and applications in supervised and unsupervised machine learning
• linking artificial intelligence with stochastic differential equations

• Stochastic Differential Equations and Their Applications in Mathematics (5 articles)
• Stochastic Differential Equations and Their Applications 2020 in Mathematics (5 articles)