Related papers: Characterization of unitary processes with indepen…

We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…

We consider a particle system with weights and the scaling limits derived from its occupation time. We let the particles perform independent recurrent L\'evy motions and we assume that their initial positions and weights are given by a…

In this paper, we present a new approach to derive series expansions for some Gaussian processes based on harmonic analysis of their covariance function. In particular, we propose a new simple rate-optimal series expansion for fractional…

We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by…

In 3+1 space-time dimensions, fourth order derivative gravity is perturbatively renormalizable. Here it is shown that it describes a unitary theory of gravitons (with/without an additional scalar) in a limited coupling parameter space which…

Unitarity is the fundamental property of the S-matrix while its usage for a scattering of unstable particles has been subtle as unstable particles do not appear in the asymptotic states. Defining unstable-particle amplitudes as residues of…

The Hawkes process models self-exciting event streams, requiring a strictly non-negative and stable stochastic intensity. Standard identification methods enforce these properties using non-negative causal bases, yielding conservative…

We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and…

We perform the homogenization process avoiding the necessity of testing the weak formulation of the initial and homogenized systems by corresponding weak solutions. We show that the stress tensor for homogenized problem depends on the…

In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…

This paper is concerned with regularized extensions of hierarchical non-stationary temporal Gaussian processes (NSGPs) in which the parameters (e.g., length-scale) are modeled as GPs. In particular, we consider two commonly used NSGP…

We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…

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 the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…

Sublinear expectations for uncertain processes have received a lot of attention recently, particularly methods to extend a downward-continuous sublinear expectation on the bounded finitary functions to one on the non-finitary functions. In…

It is shown that the inert properties of a stationary random process can be expressed in terms of the ratio of its correlation interval to the doubled variance. When using a fixed value of the Planck constant h as a proportionality factor,…

We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures sigma (generalized spectral measures), and our focus here is on the case when the measure sigma is a singular…

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…

Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general…

In this paper, we develop two stochastic models where the variable under consideration follows Harris distribution. The mean and variance of the processes are derived and the processes are shown to be non-stationary. In the second model,…