Eigenfunction expansions for infinite dimensional Ornstein-Uhlenbeck processes
type: Item
instance of: scholarly article
title: Eigenfunction expansions for infinite dimensional Ornstein-Uhlenbeck processes
zbMATH Open document ID: 0586.60073
DOI: 10.1007/BF01845638
author: Anestis Antoniadis
author: René Carmona
publication date: 1986-01-01T00:00:00Z
review text: We give a general construction of infinite dimensional Ornstein-Uhlenbeck processes. We present expansions of these processes based on the expansion of the covariance operators in generalized eigenfunctions, and we answer positively some question left open by \textit{J. B. Walsh} [Adv. Appl. Math. 13, 231-281 (1981; Zbl 0471.60083)] on properties of the hitting times of these processes.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 3940358
zbMATH Keywords: infinite dimensional Ornstein-Uhlenbeck processes
zbMATH Keywords: expansion of the covariance operators
zbMATH Keywords: eigenfunctions
zbMATH Keywords: hitting times
MaRDI profile type: Publication
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cites work: Measurable norms and some Banach space valued Gaussian processes
cites work: Q4166947
cites work: Exponential moments for hitting times of uniformly ergodic Markov processes
cites work: Convergence en loi et lois du logarithme it�r� pour les vecteurs gaussiens
cites work: Q3205177
cites work: Stochastic evolution equations
cites work: Stochastic evolution equations and related measure processes
cites work: Large fluctuations for a nonlinear heat equation with noise
cites work: Q4096185
cites work: Q5581156
cites work: Potential theory on Hilbert space
cites work: On the formula of Mathews and Salam
cites work: Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions
cites work: Realization of Gaussian random fields
cites work: Gaussian measures in Banach spaces
cites work: Infinite dimensional Langevin equation and Fokker-Planck equation
cites work: Q5552132
cites work: Q5587587
cites work: The Ornstein-Uhlenbeck semigroup in an infinite dimensional L\(^2\) setting
cites work: The Ornstein-Uhlenbeck process as a model for neuronal activity. I. Mean and variance of the firing time
cites work: Heat conduction in solids with random external temperatures and/or random internal heat generation
cites work: Schrödinger semigroups
cites work: The Malliavin calculus and its application to second order parabolic differential equations: Part I
cites work: A stochastic model of neural response
cites work: The response of a spatially distributed neuron to white noise current injection
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3940358