26 citations · 50 across the 11 of their papers we have counts for
13 papers
On the well-posedness of (nonlinear) rough continuity equations
Lucio Galeati, James-Michael Leahy, Torstein Nilssen
Motivated by applications to fluid dynamics, we study rough differential equations (RDEs) and rough partial differential equations (RPDEs) with non-Lipschitz drifts. We prove well-…
Scaled quadratic variation for controlled rough paths and parameter estimation of fractional diffusions
James-Michael Leahy, Torstein Nilssen
We introduce the concept of finite -scaled quadratic variation along a sequence of partitions for paths on a given interval. This concept, with historical roots in the study of…
A Fisher-Rao gradient flow for entropy-regularised Markov decision processes in Polish spaces
Bekzhan Kerimkulov, James-Michael Leahy, David Siska +2
We study the global convergence of a Fisher-Rao policy gradient flow for infinite-horizon entropy-regularised Markov decision processes with Polish state and action space. The flow…
Convergence of Policy Gradient for Entropy Regularized MDPs with Neural Network Approximation in the Mean-Field Regime
Bekzhan Kerimkulov, James-Michael Leahy, David Šiška +1
We study the global convergence of policy gradient for infinite-horizon, continuous state and action space, and entropy-regularized Markov decision processes (MDPs). We consider a…
Solution properties of the incompressible Euler system with rough path advection
Dan Crisan, Darryl D. Holm, James-Michael Leahy +1
The present paper aims to establish the local well-posedness of Euler's fluid equations on geometric rough paths. In particular, we consider the Euler equations for the incompressi…
Variational principles for fluid dynamics on rough paths
Dan Crisan, Darryl D. Holm, James-Michael Leahy +1
In this paper, we introduce a new framework for parametrization schemes (PS) in GFD. Using the theory of controlled rough paths, we derive a class of rough geophysical fluid dynami…
Lagrangian averaged stochastic advection by Lie transport for fluids
Theodore D. Drivas, Darryl D. Holm, James-Michael Leahy
We formulate a class of stochastic partial differential equations based on Kelvin's circulation theorem for ideal fluids. In these models, the velocity field is randomly transporte…
On a rough perturbation of the Navier-Stokes system and its vorticity formulation
Martina Hofmanova, James-Michael Leahy, Torstein Nilssen
We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We…
On the Navier-Stokes equation perturbed by rough transport noise
Martina Hofmanová, James-Michael Leahy, Torstein Nilssen
We consider the Navier-Stokes system in two and three space dimensions perturbed by transport noise and subject to periodic boundary conditions. The noise arises from perturbing th…
On Some Properties of Space Inverses of Stochastic Flows
James-Michael Leahy, Remigijus Mikulevicius
We derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by jump SDEs with adapted coefficients in weighted Hölder norms using the Sob…
On Degenerate Linear Stochastic Evolution Equations Driven by Jump Processes
James-Michael Leahy, Remigijus Mikulevicius
We prove the existence and uniqueness of solutions of degenerate linear stochastic evolution equations driven by jump processes in a Hilbert scale using the variational framework o…
On Classical Solutions of Linear Stochastic Integro-Differential Equations
James-Michael Leahy, Remigijus Mikulevicius
We prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditionin…
Finite Difference Schemes for Linear Stochastic Integro-Differential Equations
Konstantinos Dareiotis, James-Michael Leahy
We study the rate of convergence of an explicit and an implicit-explicit finite difference scheme for linear stochastic integro-differential equations of parabolic type arising in…