10 citations · 10 across the 7 of their papers we have counts for
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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…
On the density of singular SDEs with fractional noise and applications to McKean-Vlasov equations
Lukas Anzeletti, Lucio Galeati, Alexandre Richard +1
We investigate properties of the (conditional) law of the solution to SDEs driven by fractional Brownian noise with a singular, possibly distributional, drift. Our results on the l…
Path-by-path uniqueness for stochastic differential equations under Krylov-Röckner condition
Lukas Anzeletti, Khoa Lê, Chengcheng Ling
We show that any stochastic differential equation (SDE) driven by Brownian motion with drift satisfying the Krylov-Röckner condition has exactly one solution in an ordinary sense f…
A note on weak existence for SDEs driven by fractional Brownian motion
Lukas Anzeletti
We are interested in existence of solutions to the -dimensional equation \begin{equation*} X_t=x_0+\int_0^t b(X_s)ds + B_t, \end{equation*} where is a (fractional) Brownian…
Comparison of classical and path-by-path solutions to SDEs
Lukas Anzeletti
We consider the Stochastic Differential Equation , in . We give an example of a drift such that there does not exist a wea…
Regularisation by fractional noise for one-dimensional differential equations with distributional drift
Lukas Anzeletti, Alexandre Richard, Etienne Tanré
We study existence and uniqueness of solutions to the equation , where is a distribution in some Besov space and is a fractional Brownian motion with…