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Related papers: Limit theorems for SDEs with irregular drifts

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We consider contractivity for diffusion semigroups w.r.t. Kantorovich ($L^1$ Wasserstein) distances based on appropriately chosen concave functions. These distances are inbetween total variation and usual Wasserstein distances. It is shown…

Probability · Mathematics 2015-10-20 Andreas Eberle

In this paper we establish functional Erd\H{o}s-Renyi laws for L\'evy processes, i.e. limit theorems for sets of functions on [0,1] associated to their increments. First, we determine precise conditions under which, in a general framework,…

Statistics Theory · Mathematics 2025-09-23 Dimbihery Rabenoro

In this paper we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence and uniqueness result for this class of SDEs and we present a…

Numerical Analysis · Mathematics 2018-12-12 Gunther Leobacher , Michaela Szölgyenyi

We obtain a exponential large deviation upper bound for continuous observables on suspension semiflows over a non-uniformly expanding base transformation with non-flat singularities and/or discontinuities, where the roof function defining…

Dynamical Systems · Mathematics 2019-05-21 Vitor Araujo , Andressa Souza , Edvan Trindade

The strong convergence rate of the Euler scheme for SDEs driven by additive fractional Brownian motions is studied, where the fractional Brownian motion has Hurst parameter $H\in(\frac13,\frac12)$ and the drift coefficient is not required…

Numerical Analysis · Mathematics 2022-01-19 Chuying Huang , Xu Wang

By using coupling by change of conditional probability measure, the log-Harnack inequality for path dependent McKean-Vlasov SDEs with distribution dependent diffusion coefficients is established, which together with the exponential…

Probability · Mathematics 2024-12-10 Xing Huang , Xiaochen Ma

In this paper, we consider scalar stochastic differential equations (SDEs) with a superlinearly growing and piecewise continuous drift coefficient. Existence and uniqueness of strong solutions of such SDEs are obtained. Furthermore, the…

Probability · Mathematics 2022-06-02 Huimin Hu , Siqing Gan

We study a general limiting framework for the convergence of sequences of additive functionals of diffusions to L\'evy subordinators, and provide explicit sufficient conditions that both ensure convergence and characterize the law of the…

Probability · Mathematics 2026-01-15 Thibaud Taillefumier , Gordan Zitkovic

In this paper, we are concerned with a modified Euler scheme for the SDE under consideration, where the drift is of super-linear growth and dissipative merely outside a closed ball. By adopting the synchronous coupling, along with the…

Probability · Mathematics 2025-08-12 Jianhai Bao , Jiaqing Hao

In this paper, we investigate stochastic differential equations(SDEs) driven by a class of supercritical $\alpha$-stable process(including the rotational symmetric $\alpha-$stable process) with drift $b$. The weak well-posedness is proved,…

Probability · Mathematics 2020-09-17 Guohuan Zhao

The exponential contraction in $L^1$-Wasserstein distance and exponential convergence in $L^q$-Wasserstein distance ($q\geq 1$) are considered for stochastic differential equations with irregular drift. When the irregular drift drift is…

Probability · Mathematics 2024-04-22 Shao-Qin Zhang

SDE driven by an $\alpha $-stable process, $\alpha \in \lbrack 1,2),$ with Lipshitz continuous coefficient and $\beta $-H\"older drift is considered. The existence and uniqueness of a strong solution is proved when $\beta >1-\alpha /2$ by…

Probability · Mathematics 2016-08-09 R. Mikulevicius , Fanhui Xu

In this paper, we investigate the convergence rate of the averaging principle for stochastic differential equations (SDEs) with $\beta$-H\"older drift driven by $\alpha$-stable processes. More specifically, we first derive the Schauder…

Dynamical Systems · Mathematics 2024-09-20 Mengyu Cheng , Zimo Hao , Xicheng Zhang

We study the problem of the existence, uniqueness and stability of solutions of reflected stochastic differential equations (SDEs) with a minimality condition depending on the law of the solution (and not on the paths). We require that some…

Probability · Mathematics 2020-05-26 Adrian Falkowski , Leszek Slominski

In this paper we study the rate of convergence of a symmetrized version of the Milstein scheme applied to the solution of the one dimensional SDE $$X_t = x_0 + \int_{0}^t{b(X_s)ds}+\int_{0}^t{\sigma |X_s|^\alpha dW_s}, \;x_0>0,\;\sigma>0,\;…

Probability · Mathematics 2018-11-28 Mireille Bossy , Hector Olivero Quinteros

We study the almost sure behavior of solutions of stochastic differential equations (SDEs) as time goes to zero. Our main general result establishes a functional law of the iterated logarithm (LIL) that applies in the setting of SDEs with…

Probability · Mathematics 2021-06-28 Marco Carfagnini , Juraj Foldes , David P. Herzog

We solve constrained optimal transport problems in which the marginal laws are given by the laws of solutions of stochastic differential equations (SDEs). We consider SDEs with irregular coefficients, making only minimal regularity…

Probability · Mathematics 2025-10-29 Michaela Hitz , Benjamin A. Robinson

We prove a central limit theorem characterizing the small noise fluctuations of stochastic PDEs of fluctuating hydrodynamics type. The results apply to the case of nonlinear and potentially degenerate diffusions and irregular noise…

Probability · Mathematics 2023-11-01 Andrea Clini , Benjamin Fehrman

We study pathwise approximation of strong solutions of scalar stochastic differential equations (SDEs) at a single time in the presence of discontinuities of the drift coefficient. Recently, it has been shown by M\"uller-Gronbach and…

Probability · Mathematics 2024-02-23 Simon Ellinger

Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate…

Probability · Mathematics 2022-03-16 Benjamin Fehrman , Benjamin Gess