6 papers
Uniqueness for stochastic differential equations in Hilbert spaces with irregular drift
Lukas Anzeletti, Oleg Butkovsky, Máté Gerencsér +1
We present a versatile framework to study strong existence and uniqueness for stochastic differential equations (SDEs) in Hilbert spaces with irregular drift. We consider an SDE in…
Weak existence for SDEs with singular drifts and fractional Brownian or Levy noise beyond the subcritical regime
Oleg Butkovsky, Samuel Gallay
We study a multidimensional stochastic differential equation with additive noise: \[ d X_t=b(t, X_t) dt +d ξ_t, \] where the drift is integrable in space and time, and is…
Lectures on stochastic sewing with applications
Oleg Butkovsky
These are lecture notes for a mini-course on stochastic sewing, taught at the University of Edinburgh and Beijing Institute of Technology in Spring/Summer 2025. The aim is to intro…
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 $…
Stochastic equations with singular drift driven by fractional Brownian motion
Oleg Butkovsky, Khoa Lê, Leonid Mytnik
We consider stochastic differential equation where the drift is either a measure or an integrable function, and is a -dimensional fract…