5 papers
Uniform in time convergence of numerical schemes for stochastic differential equations via Strong Exponential stability: Euler methods, Split-Step and Tamed Schemes
Letizia Angeli, Dan Crisan, Michela Ottobre
We prove a general criterion providing sufficient conditions under which a time-discretiziation of a given Stochastic Differential Equation (SDE) is a uniform in time approximation…
Spatial analyticity and exponential decay of Fourier modes for the stochastic Navier-Stokes equation
Dan Crisan, Prince Romeo Mensah
We construct a local in time spatially real-analytic solution to the 2D and 3D stochastic Navier--Stokes equation driven by a spatially real-analytic multiplicative and transport n…
Poisson Equations with locally-Lipschitz coefficients and Uniform in Time Averaging for Stochastic Differential Equations via Strong Exponential Stability
Dan Crisan, Paul Dobson, Ben Goddard +2
We study averaging for Stochastic Differential Equations (SDEs) and Poisson equations. We succeed in obtaining a uniform in time (UiT) averaging result, with a rate, for fully coup…
Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations
Hamza Ruzayqat, Alexandros Beskos, Dan Crisan +2
We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This…
Sequential discretisation schemes for a class of stochastic differential equations and their application to Bayesian filtering
Deniz Akyildiz, Dan Crisan, Joaquin Miguez
We introduce a predictor-corrector discretisation scheme for the numerical integration of a class of stochastic differential equations and prove that it converges with weak order 1…