Markov chain approximations to stochastic differential equations by recombination on lattice trees by Cosentino, F, Oberhauser, H, Abate, A

“…We revisit the classical problem of approximating a stochastic differential equation by a discrete-time and discrete-space Markov chain. …”

Learning stochastic differential equations using RNN with log signature features by Liao, S, Lyons, T, Yang, W, Ni, H

The random periodic solution of a stochastic differential equation with a monotone drift and its numerical approximation by Wu, Y

“…In this paper we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with a one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical approximation via the backward Euler-Maruyama method. …”

Semi-implicit Taylor schemes for stiff rough differential equations by Riedel, S, Wu, Yue

“…We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. …”

Grid-free computation of probabilistic safety with Malliavin Calculus by Cosentino, F, Oberhauser, H, Abate, A

“…This work concerns continuous-time, continuous-space stochastic dynamical systems described by stochastic differential equations (SDE). It presents a new approach to compute probabilistic safety regions, namely sets of initial conditions of the SDE associated to trajectories that are safe with a probability larger than a given threshold. …”

A stochastic model for the turbulent ocean heat flux under Arctic sea ice by Toppaladoddi, S, Wells, AJ

“…Here, we develop a model of the turbulent ice-ocean heat flux using coupled ordinary stochastic differential equations to model fluctuations in the vertical velocity and temperature in the Arctic mixed layer. …”