Stochastic differential equations (SDEs) and random processes form a central framework for modelling systems influenced by inherent uncertainties. These mathematical constructs are used to rigorously ...

The study of impulse control and stochastic differential games represents a vibrant intersection of applied mathematics and decision theory, where strategic agents operate in settings marked by ...

A new algorithm developed by Naoki Masuda, with co-athors Kazuyuki Aihara and Neil G. MacLaren, can identify the most predictive data points that a tipping point is near. Published in Nature ...

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 ...

(Conditional) generative adversarial networks (GANs) have had great success in recent years, due to their ability to approximate (conditional) distributions over extremely high-dimensional spaces.

Inspired by path integral solutions to the quantum relaxation problem, we develop a numerical method to solve classical stochastic differential equations with multiplicative noise that avoids ...

Brownian motion and Langevin's equation. Ito and Stratonovich Stochastic integrals. Stochastic calculus and Ito's formula. SDEs and PDEs of Kolmogorov. Fokker-Planck, and Dynkin. Boundary conditions, ...

Inhalt: The course “Stochastic Analysis” is for master students who are already familiar with fundamental concepts of probability theory. Stochastic analysis is a branch of probability theory that is ...

SIAM Journal on Numerical Analysis, Vol. 54, No. 2 (2016), pp. 1093-1119 (27 pages) A fully discrete approximation of the semilinear stochastic wave equation driven by multiplicative noise is ...