26 citations · 50 across the 11 of their papers we have counts for
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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…
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 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…