Related papers: On LAN for parametrized continuous periodic signal…
We consider a diffusion $(\xi_t)_{t\ge 0}$ whose drift contains some deterministic periodic signal. Its shape being fixed and known, up to scaling in time, the periodicity of the signal is the unknown parameter $\vartheta$ of interest. We…
We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity $T$ and carrying some unknown $d$-dimensional shape parameter $\theta$. We prove Local Asymptotic Normality (LAN) jointly…
Taking a multidimensional time-homogeneous dynamical system and adding a randomly perturbed time-dependent deterministic signal to some of its components gives rise to a high-dimensional system of stochastic differential equations which is…
We consider a diffusion $(\xi_t)_{t\ge 0}$ with some $T$-periodic time dependent input term contained in the drift: under an unknown parameter $\vth\in\Theta$, some discontinuity - an additional periodic signal - occurs at times…
Consider a scalar reflected diffusion $(X_t:t\geq 0)$, where the unknown drift function $b$ is modelled nonparametrically. We show that in the low frequency sampling case, when the sample consists of $(X_0,X_\Delta,...,X_{n\Delta})$ for…
We establish the local asymptotic normality (LAN) property for estimating a multidimensional parameter in the drift of a system of $N$ interacting particles observed over a fixed time horizon in a mean-field regime $N \rightarrow \infty$.…
We study statistical models for one-dimensional diffusions which are recurrent null. A first parameter in the drift is the principal one, and determines regular varying rates of convergence for the score and the information process. A…
Local Asymptotic Normality (LAN) property for fractional Gaussian noise under high-frequency observations is proved with a non-diagonal rate matrix depending on the parameter to be estimated. In contrast to the LAN families in the…
For a one dimensional diffusion process $X=\{X(t) ; 0\leq t \leq T \}$, we suppose that $X(t)$ is hidden if it is below some fixed and known threshold $\tau$, but otherwise it is visible. This means a partially hidden diffusion process. The…
Suppose we have a high-frequency sample from the L\'{e}vy process of the form $X_t^\theta=\beta t+\gamma Z_t+U_t$, where $Z$ is a possibly asymmetric locally $\alpha$-stable L\'{e}vy process, and $U$ is a nuisance L\'{e}vy process less…
We study the local asymptotic normality (LAN) property for the likelihood function associated with discretely observed $d$-dimensional McKean-Vlasov stochastic differential equations over a fixed time interval. The model involves a joint…
We consider a stochastic differential equation with additive fractional noise with Hurst parameter $H>1/2$, and a non-linear drift depending on an unknown parameter. We show the Local Asymptotic Normality property (LAN) of this parametric…
In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process $X$. Our data are given by $ \int_0^1 X_{\frac{s+i}{n}} \dd \mu (s)$ for…
We study synchronization processes in networks of slightly non identical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in…
The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…
A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of…
Modeling of longitudinal data often requires diffusion models that incorporate overall time-dependent, nonlinear dynamics of multiple components and provide sufficient flexibility for subject-specific modeling. This complexity challenges…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…
We consider distributed systems with an arbitrary number of processes, modelled by timed automata that communicate through location guards: a process can take a guarded transition if at least one other process is in a given location. In…