## The Annals of Probability

### Self-Intersections and Local Nondeterminism of Gaussian Processes

Simeon M. Berman

#### 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

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