相关论文: Uniform-in-time estimates for mean-field type SDEs…

Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…

In the study of McKean-Vlasov stochastic differential equations (MV-SDEs), numerical approximation plays a crucial role in understanding the behavior of interacting particle systems (IPS). Classical Milstein schemes provide strong…

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…

This paper establishes a quantitative, uniform-in-time diffusion approximation for the joint law of a broad class of fully coupled multiscale stochastic systems. We derive a precise characterization of the limiting joint distribution as a…

In this paper, we study averaging principles for a class of time-inhomogeneous stochastic differential equations (SDEs) with slow and fast time-scales, where the drift term in the fast component is time-dependent and only partially…

This paper addresses the difficulty of characterizing the time-varying nature of fading channels. The current time-invariant models often fall short of capturing and tracking these dynamic characteristics. To overcome this limitation, we…

This paper introduces a randomized tamed Euler scheme tailored for L\'evy-driven stochastic differential equations (SDEs) with superlinear random coefficients and Carath\'eodory-type drift. Under assumptions that allow for time-irregular…

In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…

We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction potentials. The approach is based on a combination of…

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

In this paper, we aim to study the diffusion approximation for multi-scale McKean-Vlasov stochastic differential equations. More precisely, we prove the weak convergence of slow process $X^\varepsilon$ in $C([0,T];\mathbb{R}^n)$ towards the…

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…

We use the uniform semiclassical approximation in order to derive the fidelity decay in the regime of large perturbations. Numerical computations are presented which agree with our theoretical predictions. Moreover, our theory allows to…

Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical…

In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay…

This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These…

In this paper, we consider stochastic differential equations whose drift coefficient is superlinearly growing and piece-wise continuous, and whose diffusion coefficient is superlinearly growing and locally H\"older continuous. We first…

We deduce in this paper the sufficient conditions for weak convergence of centered and normed deviation of the u-statistics with values in the space of the real valued continuous function defined on some compact metric space. We obtain also…