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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.PR2026
Trimmed branching random walk and a free obstacle problem
Rami Atar, Leonid Mytnik, Gershon Wolansky
Consider particles performing random walks on the -grid , with branching and density-dependent selection: When one of the particles branches, a particle is rem…