Ergodicity of stochastic differential equations with jumps and singular coefficients

L Xie, X Zhang - 2020 - projecteuclid.org
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 …

Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness

L Beck, F Flandoli, M Gubinelli, M Maurelli - 2019 - projecteuclid.org
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 …

Schauder estimates for drifted fractional operators in the supercritical case

PÉC de Raynal, S Menozzi, E Priola - Journal of Functional Analysis, 2020 - Elsevier
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 …

Regularity of local times associated with Volterra–Lévy processes and path-wise regularization of stochastic differential equations

FA Harang, C Ling - Journal of Theoretical Probability, 2022 - Springer
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 …

Strong existence and uniqueness for stable stochastic differential equations with distributional drift

S Athreya, O Butkovsky, L Mytnik - The Annals of Probability, 2020 - JSTOR
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 …

[HTML][HTML] Schauder estimates for nonlocal kinetic equations and applications

Z Hao, M Wu, X Zhang - Journal de Mathématiques Pures et Appliquées, 2020 - Elsevier
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 …

Strong rate of convergence of the Euler scheme for SDEs with irregular drift driven by Levy noise

O Butkovsky, K Dareiotis, M Gerencsér - arXiv preprint arXiv:2204.12926, 2022 - arxiv.org
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 …

Well-posedness of some non-linear stable driven SDEs

N Frikha, V Konakov, S Menozzi - arXiv preprint arXiv:1910.05945, 2019 - arxiv.org
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

O Butkovsky, L Mytnik - 2019 - projecteuclid.org
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 …

[PDF][PDF] Smoothness of solutions of hyperbolic stochastic partial differential equations with L∞-vector fields

AM Bogso, M Dieye, O Menoukeu Pamen… - arXiv preprint arXiv …, 2022 - researchgate.net
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 …