Large deviations for Brownian intersection measures
- König, Wolfgang
- Mukherjee, Chiranjib
DOIAbstract
We consider $p$ independent Brownian motions in $R^d$. We assume that $pgeq 2$ and $p(d-2)<d$. Let $ell_t$ denote the intersection measure of the $p$ paths by time $t$, i.e., the random measure on $R^d$ that assigns to any measurable set $Asubset R^d$ the amount of intersection local time of the motions spent in $A$ by time $t$. Earlier results of Chen citeCh09 derived the logarithmic asymptotics of the upper tails of the total mass $ell_t(R^d)$ as $ttoinfty$. In this paper, we derive a large-deviation principle for the normalised intersection measure $t^-pell_t$ on the set of positive measures on some open bounded set $BsubsetR^d$ as $ttoinfty$ before exiting $B$. The rate function is explicit and gives some rigorous meaning, in this asymp...
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