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Infinite Dimensional Piecewise Deterministic Markov Processes
Paul Dobson, Joris Bierkens
In this paper we aim to construct infinite dimensional versions of well established Piecewise Deterministic Monte Carlo methods, such as the Bouncy Particle Sampler, the Zig-Zag Sa…
Subgeometric hypocoercivity for piecewise-deterministic Markov process Monte Carlo methods
Christophe Andrieu, Paul Dobson, Andi Q. Wang
We extend the hypocoercivity framework for piecewise-deterministic Markov process (PDMP) Monte Carlo established in [Andrieu et. al. (2018)] to heavy-tailed target distributions, w…
Uniform in time estimates for the weak error of the Euler method for SDEs and a Pathwise Approach to Derivative Estimates for Diffusion Semigroups
D. Crisan, P. Dobson, M. Ottobre
We present a criterion for uniform in time convergence of the weak error of the Euler scheme for Stochastic Differential equations (SDEs). The criterion requires i) exponential dec…
Long-time behaviour of degenerate diffusions: UFG-type SDEs and time-inhomogeneous hypoelliptic processes
T. Cass, D. Crisan, P. Dobson +1
We study the long time behaviour of a large class of diffusion processes on , generated by second order differential operators of (possibly) degenerate type. The operators tha…