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 ...

Stochastic fluid dynamics extends classical fluid mechanics by incorporating randomness and uncertainty directly into the governing equations. This approach utilises stochastic differential equations ...

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 ...

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 ...

(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 ...

This is a preview. Log in through your library . Abstract We study the weak solution X of a parabolic stochastic partial differential equation driven by two independent processes: a Gaussian white ...

This is a preview. Log in through your library . Abstract We consider numerical schemes for simulating diffusions that evolve in SO(n) and SE(n). Surprisingly, schemes based on the exponential ...

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 ...