Related papers: Asymptotic statistical equivalence for ergodic dif…
We study the asymptotic behaviour of a real-valued diffusion whose non-regular drift is given as a sum of a dissipative term and a bounded measurable one. We prove that two trajectories of that diffusion converge a.s. to one another at an…
We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini's mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic,…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore…
Consider a piecewise smooth expanding map of the interval possessing several invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs). After this system is perturbed to make the…
We are interested in a non-local partial differential equation modeling equal mitosis. We prove that the solutions present persistent asymptoticoscillations and that the convergence to this periodic behavior, in suitable spaces of weighted…
In order to sample from a given target distribution (often of Gibbs type), the Monte Carlo Markov chain method consists in constructing an ergodic Markov process whose invariant measure is the target distribution. By sampling the Markov…
We consider the problem of detecting a rectangle of activation in a grid of sensors in d-dimensions with noisy measurements. This has applications to massive surveillance projects and anomaly detection in large datasets in which one detects…
We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit…
The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…
We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e.,…
We consider a piecewise smooth expanding map of the interval possessing two invariant subsets of positive Lebesgue measure and exactly two ergodic absolutely continuous invariant probability measures (ACIMs). When this system is perturbed…
We consider a nonstationary sequence of independent random isometries of a compact metrizable space. Assuming that there are no proper closed subsets with deterministic image we establish a weak-* convergence to the unique invariant under…
We recall the main concepts of the Le Cam theory of statistical experiments , especially the notion of Le Cam distance and its properties. We also review classical tools for bounding such a distance before presenting some examples. A proof…
We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if…
We investigate the asymptotic behavior of several variants of the scan statistic applied to empirical distributions, which can be applied to detect the presence of an anomalous interval with any length. Of particular interest is Studentized…
This report compares two tests of second-order stationarity through simulation. It also provides several examples of localised autocovariances and their approximate confidence intervals on different real and simulated data sets. An…
We derive an asymptotic log-Harnack inequality for nonlinear monotone SPDE driven by possibly degenerate multiplicative noise. Our main tool is the asymptotic coupling by the change of measure. As an application, we show that, under certain…
Quasi-invariant measures for non-discrete groups of diffeomorphisms containing a Morse-Smale dynamics are studied. The assumption concerning the presence of a Morse-Smale dynamics allows us to extend to higher dimensions a number of…
When a parameter of interest is defined to be a nondifferentiable transform of a regular parameter, the parameter does not have an influence function, rendering the existing theory of semiparametric efficient estimation inapplicable.…