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.
Citation
Simeon M. Berman. "Self-Intersections and Local Nondeterminism of Gaussian Processes." Ann. Probab. 19 (1) 160 - 191, January, 1991. https://doi.org/10.1214/aop/1176990539
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