Analog of heat equation for Gaussian measure of a ball in Hilbert space
type: Item
instance of: scholarly article
title: Analog of heat equation for Gaussian measure of a ball in Hilbert space
zbMATH Open document ID: 0708.60002
DOI: 10.1007/BF01046096
author: Gyula Pap
published in: Journal of Theoretical Probability
publication date: 1990-01-01T00:00:00Z
review text: Let \(\mu\) be a Gaussian measure on a separable Hilbert space H with mean vector a and covariance operator T. If g(a,T) is the value of \(\mu\) on a fixed open ball in H, then it is well known that g(,T) is Gateaux differentiable with respect to a. The author proves that g(a,) is also differentiable with respect to all covariance operators T on H and moreover, that the function g(a,T) satisfies the heat equation in a sense which is specified in the paper.
Mathematics Subject Classification ID: 60B05
zbMATH DE Number: 4163794
zbMATH Keywords: heat equation
zbMATH Keywords: Gaussian measure on a separable Hilbert space
zbMATH Keywords: covariance operator
zbMATH Keywords: Gateaux differentiable
MaRDI profile type: Publication
cites work: Q3324720
cites work: Q5565769
cites work: Q5336643
cites work: Gaussian measures in Banach spaces
cites work: Gaussian Measure of Translated Balls in a Banach Space
cites work: Q3041461
full work available at URL: https://doi.org/10.1007/bf01046096
OpenAlex ID: W2003220521
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description: scientific article; zbMATH DE number 4163794