Thomas Hughes

collaborators

3 papers

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…

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

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