7 papers
On the existence of Markovian measures on continuous paths
Jules Pitcho
Let be a positive Radon measure on the space of continuous paths from R into a locally compact Polish space , and assume that admits an invariant measure.…
On the zero-noise limit for SDE's singular at the initial time
Jules Pitcho
We investigate the zero-noise limit for SDE's driven by Brownian motion with a divergence-free drift singular at the initial time and prove that a unique probability measure concen…
On vanishing diffusivity selection for the advection equation
Giulia Mescolini, Jules Pitcho, Massimo Sorella
We study the advection equation along vector fields singular at the initial time. More precisely, we prove that for divergence-free vector fields in $L^1_{loc}((0, T ]; BV (\mathbb…
On the stochastic selection of integral curves of a rough vector field
Jules Pitcho
We prove that for bounded, divergence-free vector fields b in L^1_{loc}((0,1];BV(\T^d;\R^d)), there exists a unique incompressible measure on integral curves of b. We recall the ve…
On the lack of selection for the transport equation over a dense set of vector fields
Jules Pitcho
We construct a set of bounded vector fields dense in for and with for which smooth regu…
A remark on selection of solutions for the transport equation
Jules Pitcho
We prove that for bounded, divergence-free vector fields in , regularisation by convolution of the vector field selects a single solution…
Almost everywhere non-uniqueness of integral curves for divergence-free Sobolev vector fields
J. Pitcho, M. Sorella
We construct divergence-free Sobolev vector fields in C([0,1];W^{1,r}(T^d;R^d)) with r < d and d >=2 which simultaneously admit any finite number of distinct positive solutions to…