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Rate of explosion of the Amperean area of the planar Brownian loop. (English) Zbl 0814.60081

Azéma, Jacques (ed.) et al., Séminaire de Probabilités XXVIII. Berlin: Springer-Verlag. Lect. Notes Math. 1583, 153-163 (1994).
The main result proved is \[ \lim_{\varepsilon \to 0} {1 \over | \log \varepsilon |} \int(n_ z)^ 2 dz = {1 \over 2 \pi}, \] where \(dz\) is Lebesgue measure on \(\mathbb{R}^ 2\) and \(n_ z\) in the “index” of the two-dimensional Brownian motion around \(z\).
For the entire collection see [Zbl 0797.00020].

MSC:

60J65 Brownian motion
60H05 Stochastic integrals
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