Related papers: Stationary random fields with linear regressions

This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…

We present a simple approach to discrete q-Hermite polynomials with special emphasis on analogies with the classical case.

In this note, we consider general growth-fragmentation equations from a probabilistic point of view. Using Foster-Lyapunov techniques, we study the recurrence of the associated Markov process depending on the growth and fragmentation rates.…

Let $\mathbb{R}^N_+= [0,\infty)^N$. We here consider a class of random fields $(X_t)_{t\in \mathbb{R}^N_+}$ which are known as Multiparameter L\'evy processes. Related multiparameter semigroups of operators and their generators are…

We consider some discrete $q$-analogues of the classical continuous orthogonal polynomial ensembles. Building on results due to Morozov, Popolitov and Shakirov, we find representations for the moments of the discrete $q$-Hermite and…

In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…

Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we…

We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…

We characterize the atomic probability measure on $\mathbb{R}^d$ which having a finite number of atoms. We further prove that the Jacobi sequences associated to the multiple Hermite (resp. Laguerre, resp. Jacobi) orthogonal polynomials are…

Let $(Z^{q, H}_t)_{t \in [0, 1]^d}$ denote a $d$-parameter Hermite random field of order $q \geq 1$ and self-similarity parameter $H = (H_1, \ldots, H_d) \in (\frac{1}{2}, 1)^d$. This process is $H$-self-similar, has stationary increments…

We establish a connection between the structure of a stationary symmetric alpha-stable random field (0 < alpha < 2) and ergodic theory of non-singular group actions, elaborating on a previous work by Rosinski (2000). With the help of this…

We consider the piecewise-deterministic Markov process obtained by randomly switching between the flows generated by a finite set of smooth vector fields on a compact set. We obtain H\"ormander-type conditions on the vector fields…

Switching ARMA models greatly enhance the standard linear models to the extent that different ARMA model is allowed in a different regime, and the regime switching is typically assumed a Markov chain on the finite states of potential…

We consider a Markov process on non-negative integer arrays of a certain shape, this shape being determined by general parameters in the model which correspond to drifts. In the case where these drifts are trivial, the arrays are reverse…

We reexamine the connection between spin and statistics through the quantization of a complex scalar field, using the formulation with the property that the hermitian conjugate of canonical momentum for a variable is just the canonical…

We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary…

In this article, we characterize continuous stationary fields via generalized Langevin dynamics. This gives natural connections between stationary fields, stationary increment fields, self-similar fields, and generalized Langevin dynamics.…

We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…

We consider an intersection of past and future property of multivariate stationary processes which is the key to deriving various representation theorems for their linear predictor coefficient matrices. We extend useful spectral…

In this paper we prove the Poisson Hypothesis for the limiting behavior of the large queueing systems in some simple ("mean-field") cases. We show in particular that the corresponding dynamical systems, defined by the non-linear Markov…