Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

We will present stochastic dynamical models via stochastic differential equations and study existence and uniqueness of solutions, linear stochastic differential equations, theory for diffusion ...

In this paper, we focus on a new type of backward stochastic differential equations called reflected mean-field backward stochastic differential equations with time delayed generators (reflected ...

Chapter 1: Stochastic Variables and Stochastic Processes (352 KB) Contents: Stochastic Variables and Stochastic Processes Stochastic Differential Equations The Fokker–Planck Equation Advanced Topics ...

In this technical note, we discuss the stochastic optimal control problems of mean-field stochastic differential delayed equations (MFSDDEs) which arise naturally from various backgrounds including ...

Abstract Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Lévy processes and have wide applications in engineering ...

A collection of resources regarding the interplay between differential equations, deep learning, dynamical systems, control and numerical methods.

Despite this diversity in the origins of noisy oscillations, each of the mechanisms above can be instantiated as a Markov process, for example, as a system of stochastic differential equations.

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The Department of Mathematics and Statistics was host until 2014 to the MSc course in the Mathematics of Scientific and Industrial Computation (previously known as Numerical Solution of Differential ...