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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 $…
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…
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…
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}Δu_…