4 papers
Rough stochastic differential equations
Peter K. Friz, Antoine Hocquet, Khoa Lê
We establish a simultaneous generalization of Itô's theory of stochastic and Lyons' theory of rough differential equations. The interest in such a unification comes from a variety…
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…
Taming singular stochastic differential equations: A numerical method
Khoa Lê, Chengcheng Ling
We consider a generic and explicit tamed Euler--Maruyama scheme for multidimensional time-inhomogeneous stochastic differential equations with multiplicative Brownian noise. The di…
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…