Related papers: Permanental Processes
Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…
The goal of this paper is to understand the conditional law of a stochastic process once it has been observed over an interval. To make this precise, we introduce the notion of a continuous disintegration: a regular conditional probability…
A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output of a set of linear fractional stochastic…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
We consider prediction theory for stationary stochastic processes in continuous time. We discuss prediction using the whole (infinite) past, and using only a finite section of the past. The solutions to both these classical problems have…
A new notion of stochastic germs for quantum processes is introduced and a characterisation of the stochastic differentials for positive definite (PD) processes is found in terms of their germs for arbitrary Ito algebra. A representation…
From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly…
In this paper analogically as quadratic stochastic operators and processes we define cubic stochastic operator (CSO) and cubic stochastic processes (CSP). These are defined on the set of all probability measures of a measurable space. The…
We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_p(\mathbb {T}),\,p\geq1$, is constructed.
We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…
A generalized matrix function is a generalization of determinant and permanent function. In this paper, we introduced the formula for the value of a generalized matrix function of a linear sum of permutation matrices. We show that a linear…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
In this paper, we adopt a Bayesian point of view for predicting real continuous-time processes. We give two equivalent definitions of a Bayesian predictor and study some properties: admissibility, prediction sufficiency, non-unbiasedness,…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the…
Consider the following stochastic partial differential equation, \begin{equation*} \partial_t u_t(x)= \mathcal{L}u_t(x)+ \sigma (u_t(x))\dot F(t,x)\quad{t>0}\quad\text{and}\quad x\in R^d. \end{equation*} The operator $\mathcal{L}$ is the…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…
In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…