Self-Intersections and Local Nondeterminism of Gaussian Processes

Let X(t), t ≥ 0, be a vector Gaussian process in Rmwhose components are i.i.d. copies of a real Gaussian process X(t) with stationary increments. Under specified conditions on the spectral distribution function used in the representation of the incremental variance function, it is shown that the sel...

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Bibliographic Details
Published in:The Annals of probability 1991-01, Vol.19 (1), p.160-191
Main Author: Berman, Simeon M.
Format: Article
Language:English
Subjects:
60G15
60G17
60J55
Coefficients
Covariance
Eigenfunctions
Exact sciences and technology
Fourier series
Gaussian processes
Intersections of sample paths
local nondeterminism
local time
Mathematical constants
Mathematical functions
Mathematical theorems
Mathematical vectors
Mathematics
Probability and statistics
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
spectral distribution
Stochastic processes
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Summary:Let X(t), t ≥ 0, be a vector Gaussian process in Rmwhose components are i.i.d. copies of a real Gaussian process X(t) with stationary increments. Under specified conditions on the spectral distribution function used in the representation of the incremental variance function, it is shown that the self-intersection local time of multiplicity r of the vector process is jointly continuous. The dimension of the self-intersection set is estimated from above and below. The main tool is the concept of local nondeterminism.
ISSN:0091-1798
2168-894X
DOI:10.1214/aop/1176990539