7 papers · 1 filter
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…
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…
Uniqueness and Longtime Behavior of the Completely Positively Correlated Symbiotic Branching Model
Eran Avneri, Leonid Mytnik
The symbiotic branching model in describes the behavior of two branching populations migrating in space in terms of a corresponding system of stochastic p…
Weak uniqueness for singular stochastic equations
Oleg Butkovsky, Leonid Mytnik
We put forward a new method for proving weak uniqueness of stochastic equations with singular drifts driven by a non-Markov or infinite-dimensional noise. We apply our method to st…
Analytically weak and mild solutions to stochastic heat equation with irregular drift
Siva Athreya, Oleg Butkovsky, Khoa Lê +1
Consider the stochastic heat equation \begin{equation*} \partial_t u_t(x)=\frac12 \partial^2_{xx}u_t(x) +b(u_t(x))+\dot{W}_{t}(x),\quad t\in(0,T],\, x\in D, \end{equation*} where $…
Wright-Fisher stochastic heat equations with irregular drifts
Clayton Barnes, Leonid Mytnik, Zhenyao Sun
Consider the -valued continuous random field solution to the one-dimensional stochastic heat equation \[ \partial_t u_t = \frac{1}{2}Îu…