Related papers: Characterization of positively correlated squared …
We investigate integrability properties of processes with linear regressions and quadratic conditional variances. We establish the right order of dependence of which moments are finite on the parameter defined below, raising the question of…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
I comment on a recent paper by Ruiz and Tsallis [Phys. Lett. A 376, 2451 (2012)] claiming to have found a '$q$-exponential' generalization of the large deviation principle for strongly correlated random variables. I show that the basic…
We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.
The Cox process is a stochastic process which generalises the Poisson process by letting the underlying intensity function itself be a stochastic process. In this paper we present a fast Bayesian inference scheme for the permanental…
A new stochastic process is introduced and considered - squared Bessel process with special stochastic time. The analogues of fundamental properties for Brownian motion are deduced for squared Bessel process. In particular an analogue of…
Gaussian correlation conjecture states that the Gaussian measure of the intersection of two symmetric convex sets is greater or equal to the product of the measures.
We obtain series expansions of the $q$-scale functions of arbitrary spectrally negative L\'evy processes, including processes with infinite jump activity, and use these to derive various new examples of explicit $q$-scale functions.…
For log-correlated Gaussian fields on $\mathbb{R}^d$ with $d \geq 2$, Ding-Gwynne-Zhuang (2023) established the existence of subsequential limits of exponential metrics obtained from appropriate approximations. For $\gamma \in…
Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…
Given random variables $X$ and $Y$ having finite moments of all orders, their uncorrelatedness set is defined as the set of all pairs $(j,k)\in{\mathbb N}^2,$ for which $X^j$ and $Y^k$ are uncorrelated. It is known that, broadly put, any…
It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to…
Complex multivariate time series arise in many fields, ranging from computer vision to robotics or medicine. Often we are interested in the independent underlying factors that give rise to the high-dimensional data we are observing. While…
We consider a particle system of the squared Bessel processes with index $\nu > -1$ conditioned never to collide with each other, in which if $-1 < \nu < 0$ the origin is assumed to be reflecting. When the number of particles is finite, we…
Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…
Quantumness and separability criteria for continuous variable systems are discussed for the case of a noncommutative (NC) phase-space. In particular, the quantum nature and the entanglement configuration of NC two-mode Gaussian states are…
In this work, we study the properties of a pentadiagonal symmetric matrix with perturbed corners. More specifically, we present explicit expressions for characterizing when this matrix is non-negative and positive definite in two special…
Gel'fand triples of test and generalized functionals in Gaussian spaces are constructed and characterized.
We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is…
Extensions and variants are given for the well-known comparison principle for Gaussian processes based on ordering by pairwise distance.