Résumé
Nous étudions le comportement asymptotique de l'aireA n de l'ensemble des points autour desquels le mouvement brownien plan a tourné environn fois sur un intervalle de temps fixé [0,t]. Nous montrons en particulier que lorsquen tend vers l'infini,A n est équivalent dansL 2 àt/(2πn 2) asn
Summary
We study the asymptotic behaviour of the areaA n of the set of points around which the planar Brownian motion winds about n times on a given timeinterval [0,t]. We prove thatA n is equivalent (in theL 2-sense) tot/(2πn 2) asn tends to infinity.
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Werner, W. Sur les points autour desquels le mouvement brownien plan tourne beaucoup. Probab. Th. Rel. Fields 99, 111–144 (1994). https://doi.org/10.1007/BF01199592
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DOI: https://doi.org/10.1007/BF01199592
Mathematics Subject Classification (1991)
- 60J65