3 papers
math.PR2026
Compact Support Property of Super-Brownian Motion with Irregular Drift
Leonid Mytnik, Johanna Weinberger
We study the one-dimensional stochastic partial differential equation \[ d_t X_t(x)=\frac{1}{2}ΔX_t(x) +b_1\unicode{x1D7D9}_{\{X_t(x)>0\}} +\sqrt{X_t(x)}\dot W(t,x), \] where $b_1>…
math.PR2025
Weak Existence and Uniqueness for Super-Brownian Motion with Irregular Drift
Leonid Mytnik, Johanna Weinberger
We establish weak existence and uniqueness for random field solutions of the one-dimensional SPDE \[ d_tX_t = \frac{1}{2}ΔX_t +h(X_t)+ \sqrt{X_t}\dot{W}, \quad t\geq 0,\] where $\d…
math.PR2024
Strong Existence and Uniqueness for Singular SDEs Driven by Stable Processes
Leonid Mytnik, Johanna Weinberger
We consider the one-dimensional stochastic differential equation \begin{equation*} X_t = x_0 + L_t + \int_0^t μ(X_s)ds, \quad t \geq 0, \end{equation*} where is a finite measur…