The Annals of Probability

Self-Intersections and Local Nondeterminism of Gaussian Processes

Simeon M. Berman

Full-text: Open access

Abstract

Let $\mathbf{X}(t), t \geq 0$, be a vector Gaussian process in $R^m$ whose 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.

Article information

Source
Ann. Probab., Volume 19, Number 1 (1991), 160-191.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990539

Digital Object Identifier
doi:10.1214/aop/1176990539

Mathematical Reviews number (MathSciNet)
MR1085331

Zentralblatt MATH identifier
0728.60037

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G17: Sample path properties 60J55: Local time and additive functionals

Keywords
Intersections of sample paths local nondeterminism local time Gaussian processes spectral distribution

Citation

Berman, Simeon M. Self-Intersections and Local Nondeterminism of Gaussian Processes. Ann. Probab. 19 (1991), no. 1, 160--191. doi:10.1214/aop/1176990539. https://projecteuclid.org/euclid.aop/1176990539


Export citation