Related papers: Asymptotic Stability of Empirical Processes and Re…
We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
Under a regularity assumption we prove that reachability in fixed time for nonlinear control systems is robust under control sampling.
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
Certain extremum estimators have asymptotic distributions that are non-Gaussian, yet characterizable as the distribution of the $\argmax$ of a Gaussian process. This paper presents high-level sufficient conditions under which such…
In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certified by the stability theorem…
We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to…
We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…
For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…
Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…
We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard…
The recent argue about the existence of an instability in the definition of the mean value appearing in the Tsallis non extensive Statistical Mechanic is reconsidered. Here, it is simply underlined that the pair of probability distributions…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
This paper considers the problem of testing if a sequence of means $(\mu_t)_{t =1,\ldots ,n }$ of a non-stationary time series $(X_t)_{t =1,\ldots ,n }$ is stable in the sense that the difference of the means $\mu_1$ and $\mu_t$ between the…
It is a known fact that not all controllable systems can be asymptotically stabilized by a continuous static feedback. Several approaches have been developed throughout the last decades, including time-varying, dynamical and even…
In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…
We investigate the asymptotic behavior, in the long time limit, of the random homology associated to realizations of stochastic diffusion processes on a compact Riemannian manifold. In particular a rigidity result is established: if the…