Jules Pitcho

collaborators

4 papers

math.AP2026

On the existence of Markovian measures on continuous paths

Jules Pitcho

Let $I^\cdot$ be a positive Radon measure on the space of continuous paths from R into a locally compact Polish space $Y$ , and assume that $I^\cdot$ admits an invariant measure…

math.PR2025

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…

math.AP2025

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…

math.AP2025

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 $L^{p} ((0, 2); W_{l oc}^{s, p} (R^{2}; R^{2}))$ for $1 \leq p < + \infty$ and $0 \leq s < 1$ with $p < 1/ s$ for which smooth regu…