Abstract
A celebrated theorem of Spitzer suggests that the number of windings made by a planar Brownian motion Z around the origin and taken in the logarithmic time-scale, is asymptotically close to a Cauchy process. The purpose of this paper is to show that this informal consideration can be made precise by introducing the Ornstein-Uhlenbeck process X(t)=e −t/2Z(et). This yields short proofs of known results as well as some new features on the asymptotic behaviour of the winding number (in distribution and pathwise).
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© 1994 Springer-Verlag
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Bertoin, J., Werner, W. (1994). Asymptotic windings of planar Brownian motion revisited via the Ornstein-Uhlenbeck process. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXVIII. Lecture Notes in Mathematics, vol 1583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073842
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DOI: https://doi.org/10.1007/BFb0073842
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