We show the strong well-posedness of SDEs driven by general multiplicative Lévy noises
with Sobolev diffusion and jump coefficients and integrable drifts. Moreover, we also study …

In this paper linear stochastic transport and continuity equations with drift in critical L^p
spaces are considered. In this situation noise prevents shocks for the transport equation and …

We consider a non-local operator L α which is the sum of a fractional Laplacian△ α/2, α∈(0,
1), plus a first order term which is measurable in the time variable and locally β-Hölder …

We investigate the space-time regularity of the local time associated with Volterra–Lévy
processes, including Volterra processes driven by α α-stable processes for α ∈ (0, 2 α∈(0 …

We consider the stochastic differential equation dXt= b (Xt) dt+ dLt, where the drift b is a
generalized function and L is a symmetric one dimensional α-stable Lévy processes, α∈(1 …

In this paper we develop a new method based on Littlewood-Paley's decomposition and
heat kernel estimates in integral form, to establish Schauder's estimate for the following …

We study the strong rate of convergence of the Euler--Maruyama scheme for a
multidimensional stochastic differential equation (SDE) $$ dX_t= b (X_t) dt+ dL_t, $$ with …

We prove the well-posedness of some non-linear stochastic differential equations in the
sense of McKean-Vlasov driven by non-degenerate symmetric $\alpha $-stable L\'evy …

Regularization by noise and flows of solutions for a stochastic heat equation Page 1 The Annals
of Probability 2019, Vol. 47, No. 1, 165–212 https://doi.org/10.1214/18-AOP1259 © Institute of …

In this paper we are interested in a quasi-linear hyperbolic stochastic differential equation
(HSPDE) when the vector field is merely bounded and measurable. Although the …