Stochastic optimal control combined with partial differential equations (PDEs) represents a robust framework for managing systems influenced by inherent uncertainties and spatial-temporal dynamics.

This is a preview. Log in through your library . Abstract In this paper, we introduce a Wasserstein-type distance on the set of the probability distributions of strong solutions to stochastic ...

We consider a stochastic partial differential equation with reflection at 0 and with the constraint of conservation of the space average. The equation is driven by the derivative in space of a ...

The stochastic Cahn–Hilliard equation is a pivotal tool in modelling phase separation and pattern formation in complex systems such as binary mixtures and alloys. By introducing stochastic ...

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...

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 ...