Related papers: On stationarity properties of generalized Hermite-…
We consider a three-dimensional Fourier integral in which the exponent in the exponential factor is the product of some phase function and a large parameter. The asymptotics of this integral is sought when the large parameter tends to…
The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…
We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…
Let $(X_j)_{j\geq1}$ be a multivariate long-range dependent Gaussian process. We study the asymptotic behavior of the corresponding sequential empirical process indexed by a class of functions. If some entropy condition is satisfied we have…
We study a class of deterministic flows in ${\mathbb R}^{d\times k}$, parametrized by a random matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d}$ with i.i.d. centered subgaussian entries. We characterize the asymptotic behavior of these…
It is shown how the central limit theorem for U-statistics of spatial Poisson point processes can help to derive the central limit theorem for U-statistics of a Gibbs facet process from stochastic geometry. A full-dimensional submodel…
In the framework of quasi-Hermitian quantum mechanics it is shown that a weakening of the isotropy of the Hilbert-space geometry can help us to enlarge the domain of the parameters at which the evolution is unitary. The idea is tested using…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
We study the limit law of a vector made up of normalized sums of functions of long-range dependent stationary Gaussian series. Depending on the memory parameter of the Gaussian series and on the Hermite ranks of the functions, the resulting…
In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…
We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric stable non-Gaussian discrete-parameter random field using the framework of Hult and Samorodnitsky (2010). Depending on the ergodic…
Long-range dependent random fields with spectral densities which are unbounded at some frequencies are investigated. We demonstrate new examples of covariance functions which do not exhibit regular varying asymptotic behaviour at infinity.…
This paper deals with the asymptotic behavior of random oscillatory integrals in the presence of long-range dependence. As a byproduct, we solve the corrector problem in random homogenization of one-dimensional elliptic equations with…
In this note we describe some results concerning non-relativistic quantum systems at positive temperature and density confined to macroscopically large regions of physical space which are under the influence of some local, time-dependent…
We derive a nonparametric higher-order asymptotic expansion for small-time changes of conditional characteristic functions of It\^o semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of…
In this paper, we show that three different generalized similarities enclose all unitary and anti-unitary symmetries that induce exceptional points in lower-dimensional non-Hermitian systems. We prove that the generalized similarity…
We discuss the time evolution of physical finite dimensional systems which are modelled by non-hermitian Hamiltonians. We address both general non-hermitian Hamiltonians and pseudo-hermitian ones. We apply the theory of Krein Spaces to…
In this paper we study the asymptotic behavior of linear processes having as innovations mean zero, square integrable functions of stationary reversible Markov chains. In doing so we shall preserve the generality of coefficients assuming…
We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…