4 papers · 1 filter
Coupled bialgebras and Lions trees
William Salkeld
A Bialgebra is a module over a ring that is both an associative algebra and a co-associative coalgebra with the product and coproduct additionally satisfying an appropriate commuta…
Higher order Lions-Taylor expansions
William Salkeld
In this paper, we provide some of the necessary mathematics to describe higher order Lions-Taylor expansions. The Lions derivative of a functional on the Wasserstein space of measu…
A Mimicking Theorem for processes driven by fractional Brownian motion
Kevin Hu, Kavita Ramanan, William Salkeld
In this paper, we prove a mimicking theorem for stochastic processes with an additive Gaussian noise along with some entropy and transport type estimates. As an application of thes…
The fundamental martingale with applications to Markov Random Fields
Kevin Hu, Kavita Ramanan, William Salkeld
We consider collections of SDEs indexed by a graph. Each SDE is driven by an additive Gaussian noise and each drift term interacts with all other SDEs within the graph neighbourhoo…