Thomas Hughes

activity

20182026

collaborators

7 papers

math.PR2026

Fluctuations for fully pushed stochastic fronts

Alison Etheridge, Raphaël Forien, Thomas Hughes +1

We study the asymptotic behaviour, in the small noise limit, of stochastic travelling wave solutions to reaction-diffusion equations perturbed by Wright-Fisher noise. Such equation…

math.PR2026

A compact support property for infinite-dimensional SDEs with Hölder continuous coefficients

Thomas Hughes, Marcel Ortgiese

We consider non-negative solutions to some infinite-dimensional SDEs on $Z^{d}$ with Hölder continuous noise coefficients. We prove that if the Hölder exponent is less than…

math.PR2022

The compact support property for solutions to stochastic heat equations with stable noise

Thomas Hughes

We consider weak non-negative solutions to the stochastic partial differential equation \[ \partial_t Y(t,x) = ΔY(t,x) + Y(t,x)^γ\dot{L}(t,x), \] for $(t,x) \in \mathbb{R}_+ \times…

math.PR2022

Instantaneous support propagation for $Λ$ -Fleming-Viot processes

Thomas Hughes, Xiaowen Zhou

For a probability-measure-valued neutral Fleming-Viot process $Z_{t}$ with Lévy mutation and resampling mechanism associated to a general $Λ$ -coalescent with multiple collisions, we…

math.PR2020

The density of the $(α, β)$ -superprocess and singular solutions to a fractional non-linear PDE

Thomas Hughes

We consider the density $X_{t} (x)$ of the critical $(α, β)$ -superprocess in $R^{d}$ with $α \in (0, 2)$ and $β < \frac{α}{d}$ . A recent result from PDE implies a dichotomy for the density: for…

math.PR2018

A Boundary Local Time For One-Dimensional Super-Brownian Motion And Applications

Thomas Hughes

For a one-dimensional super-Brownian motion with density $X (t, x)$ , we construct a random measure $L_{t}$ called the boundary local time which is supported on $\partial \{x:X(t,x) = 0…

math.PR2018

On the boundary of the zero set of super-Brownian motion and its local time

Thomas Hughes, Edwin Perkins

If $X (t, x)$ is the density of one-dimensional super-Brownian motion, we prove that $dim (\partial {x : X (t, x) > 0}) = 2 - 2 λ_{0} \in (0, 1)$ a.s. on ${X_{t} \neq = 0}$ , where $-λ_0\in(-1,-1…

Fluctuations for fully pushed stochastic fronts

A compact support property for infinite-dimensional SDEs with Hölder continuous coefficients

The compact support property for solutions to stochastic heat equations with stable noise

Instantaneous support propagation for Λ-Fleming-Viot processes

The density of the (α,β)-superprocess and singular solutions to a fractional non-linear PDE

A Boundary Local Time For One-Dimensional Super-Brownian Motion And Applications

On the boundary of the zero set of super-Brownian motion and its local time

Instantaneous support propagation for $Λ$ -Fleming-Viot processes

The density of the $(α, β)$ -superprocess and singular solutions to a fractional non-linear PDE