77 citations · 129 across the 12 of their papers we have counts for
12 papers
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…
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…
Weak error estimates for rough volatility models
Peter K. Friz, William Salkeld, Thomas Wagenhofer
We consider a class of stochastic processes with rough stochastic volatility, examples of which include the rough Bergomi and rough Stein-Stein model, that have gained considerable…
Probabilistic rough paths II Lions-Taylor expansions and Random controlled rough paths
François Delarue, William Salkeld
In line with the notion of probabilistic rough paths introduced in the previous contribution \cite{salkeld2021Probabilistic}, we address corresponding random controlled rough paths…
An example driven introduction to probabilistic rough paths
Francois Delarue, William Salkeld
In these notes, we provide an introduction to a new regularity structure used for solving rough mean-field equations. The index set of this regularity structure is described a coll…
Large Deviations and Exit-times for reflected McKean-Vlasov equations with self-stabilizing terms and superlinear drifts
Daniel Adams, Gonçalo dos Reis, Romain Ravaille +2
We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wassers…
Small ball probabilities, metric entropy and Gaussian rough paths
William Salkeld
We study the Small Ball Probabilities (SBPs) of Gaussian rough paths. While many works on rough paths study the Large Deviations Principles (LDPs) for stochastic processes driven b…
Rough functional quantization and the support of McKean-Vlasov equations
Thomas Cass, Goncalo dos Reis, William Salkeld
We prove a representation for the support of McKean Vlasov Equations. To do so, we construct functional quantizations for the law of Brownian motion as a measure over the (non-refl…
Differentiability of SDEs with drifts of super-linear growth
Peter Imkeller, Gonçalo dos Reis, William Salkeld
We close an unexpected gap in the literature of stochastic differential equations (SDEs) with drifts of super linear growth (and random coefficients), namely, we prove Malliavin an…
Freidlin-Wentzell LDP in path space for McKean-Vlasov equations and the Functional Iterated Logarithm Law
Goncalo Dos Reis, William Salkeld, Julian Tugaut
We show two Freidlin-Wentzell type Large Deviations Principles (LDP) in path space topologies (uniform and Hölder) for the solution process of McKean-Vlasov Stochastic Differential…