Related papers: The General Stationary Gaussian Markov Process

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by…

Let $W_t$ be a standard Brownian motion. It is well-known that the Langevin equation $d U_t = -\theta U_td t + d W_t$ defines a stationary process called Ornstein-Uhlenbeck process. Furthermore, Langevin equation can be used to construct…

The dynamics of a tracer particle in a stationary driven granular gas is investigated. We show how to transform the linear Boltzmann equation describing the dynamics of the tracer into a master equation for a continuous Markov process. The…

This paper investigates the Gaussian quasi-likelihood estimation of an exponentially ergodic multidimensional Markov process, which is expressed as a solution to a L\'{e}vy driven stochastic differential equation whose coefficients are…

We construct a four-parameter family of Markov processes on infinite Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary…

This paper contributes to the study of relative martingales. Specifically, for a closed random set $H$, they are processes null on $H$ which decompose as $M=m+v$, where $m$ is a c\`adl\`ag uniformly integrable martingale and, $v$ is a…

We consider a Markov chain on non-negative integer arrays of a given shape (and satisfying certain constraints) which is closely related to fundamental $SL(r+1,\mathbb{R})$ Whittaker functions and the Toda lattice. In the index zero case…

We study a decomposition of a general Markov process in a manifold invariant under a Lie group action into a radial part (transversal to orbits) and an angular part (along an orbit). We show that given a radial path, the conditioned angular…

I derive the pointwise conditional means and variances of an arbitrary Gauss-Markov process, given noisy observations of points on a sample path. These moments depend on the process's mean and covariance functions, and on the conditional…

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to…

We study the solutions of the inverse problem \[ g(z)=\int f(y) P_T(z,dy) \] for a given $g$, where $(P_t(\cdot,\cdot))_{t \geq 0}$ is the transition function of a given Markov process, $X$, and $T$ is a fixed deterministic time, which is…

Let $\eta=\{\eta(t);t\in [0,1]\}$ be a mean zero continuous Gaussian process with covariance $U=\{U(s,t),s,t\in [ 0,1]\},$ with $U(0,0)>0$. Let $\{\eta_{i};i=1,\ldots, k\}$ be independent copies of $\eta$ and set $ Y_{k}(t)=\sum_{i=1}^{k}…

We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically…

The Galton-Watson process is a Markov chain modeling the population size of independently reproducing particles giving birth to $k$ offspring with probability $p_k$, $k\ge0$. In this paper we consider {\it defective} Galton-Watson processes…

We consider a Markov process $X$ associated to a nonnecessarily symmetric Dirichlet form $\mathcal{E}$. We define a stochastic integral with respect to a class of additive functionals of zero quadratic variation and then we obtain an…

We consider two approaches to study non-reversible Markov processes, namely the Hypocoercivity Theory (HT) and GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling); the basic idea behind both of them is to split…

We derive a generalised It\=o formula for stochastic processes which are constructed by a convolution of a deterministic kernel with a centred L\'evy process. This formula has a unifying character in the sense that it contains the classical…

Starting from the forward and backward infinitesimal generators of bilateral, time-homogeneous Markov processes, the self-adjoint Hamiltonians of the generalized Schroedinger equations are first introduced by means of suitable Doob…