This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...

We show that a strongly continuous operator semigroup can be associated with the functional differential delay equation \begin{equation*}\tag{(FDE)}\begin{cases}x'(t ...

A Russian mathematician has developed a new method for analyzing a class of equations that underpin models in physics and economics and are considered "eternal" as they have challenged researchers for ...