7 citations · 8 across the 10 of their papers we have counts for
14 papers
Sticky CIR process with potential: invariant measure and exact sampling
Tony Shardlow
We study the sticky Cox--Ingersoll--Ross (CIR) process in one dimension, a diffusion on with a sticky boundary condition at the origin, arising as the marginal process…
The Regularised Inertial Dean-Kawasaki equation: discontinuous Galerkin approximation and modelling for low-density regime
Federico Cornalba, Tony Shardlow
The Regularised Inertial Dean-Kawasaki model (RIDK) -- introduced by the authors and J. Zimmer in earlier works -- is a nonlinear stochastic PDE capturing fluctuations around the m…
Deep surrogate accelerated delayed-acceptance HMC for Bayesian inference of spatio-temporal heat fluxes in rotating disc systems
Teo Deveney, Eike Mueller, Tony Shardlow
We introduce a deep learning accelerated methodology to solve PDE-based Bayesian inverse problems with guaranteed accuracy. This is motivated by the ill-posed problem of inferring…
Well-posedness for a regularised inertial Dean-Kawasaki model for slender particles in several space dimensions
Federico Cornalba, Tony Shardlow, Johannes Zimmer
A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\ma…
A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models
Teo Deveney, Eike Mueller, Tony Shardlow
We investigate a deep learning approach to efficiently perform Bayesian inference in partial differential equation (PDE) and integral equation models over potentially high-dimensio…
From weakly interacting particles to a regularised Dean--Kawasaki model
Federico Cornalba, Tony Shardlow, Johannes Zimmer
The evolution of finitely many particles obeying Langevin dynamics is described by Dean-Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative…
A walk outside spheres for the fractional Laplacian: fields and first eigenvalue
Tony Shardlow
The Feynman-Kac formula for the exterior-value problem for the fractional Laplacian leads to a walk-outside-spheres algorithm via sampling alpha-stable Levy processes on their exit…
A regularised Dean-Kawasaki model: derivation and analysis
Federico Cornalba, Tony Shardlow, Johannes Zimmer
The Dean-Kawasaki model consists of a nonlinear stochastic partial differential equation featuring a conservative, multiplicative, stochastic term with non-Lipschitz coefficient, a…
Multilevel Monte Carlo and Improved Timestepping Methods in Atmospheric Dispersion Modelling
Grigoris Katsiolides, Eike H. Müller, Robert Scheichl +3
A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent tr…
Unbiased `walk-on-spheres' Monte Carlo methods for the fractional Laplacian
Andreas E. Kyprianou, Ana Osojnik, Tony Shardlow
We consider Monte Carlo methods for simulating solutions to the analogue of the Dirichlet boundary-value problem in which the Laplacian is replaced by the fractional Laplacian and…
Gauss-quadrature method for one-dimensional mean-field SDEs
Peter Kloeden, Tony Shardlow
Mean-field SDEs, also known as McKean-Vlasov equations, are stochastic differential equations where the drift and diffusion depend on the current distribution in addition to the cu…
Langevin equations for landmark image registration with uncertainty
Stephen Marsland, Tony Shardlow
Registration of images parameterised by landmarks provides a useful method of describing shape variations by computing the minimum-energy time-dependent deformation field that flow…
On the pathwise approximation of stochastic differential equations
Tony Shardlow, Phillip Taylor
We consider one-step methods for integrating stochastic differential equations and prove pathwise convergence using ideas from rough path theory. In contrast to alternative theorie…
Improving MLMC for SDEs with application to the Langevin equation
Eike H. Mueller, Rob Scheichl, Tony Shardlow
This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the Multilevel Monte Carlo (MLMC) met…