The study of stochastic differential equations (SDEs) has long been a cornerstone in the modelling of complex systems affected by randomness. In recent years, the extension to G-Brownian motion has ...

In recent papers, McLeish and others have obtained invariance principles for weak convergence of martingales to Brownian motion. We generalize these results to prove that solutions of discrete-time ...

This is a preview. Log in through your library . Abstract We consider the stochastic sequence {Yt}t∈ N defined recursively by the linear relation Yt+1=AtYt+Bt in a random environment. The environment ...

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 ...

The paper presents a Bayesian framework for the calibration of financial models using neural stochastic differential equations (neural SDEs), for which we also formulate a global universal ...

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 ...