In this chapter, we first build upon the knowledge gained in Chapter 5 about the asymptotic windings of planar BM around one point, together with the Kallianpur-Robbins ergodic theorem for planar BM, to extend Spitzer’s theorem:
into a multidimensional result for the winding numbers (θ 1 t , θ 21 ,…, θ n t ) of planar BM around n points (all notations which may be alluded to, but not defined in this chapter are found in Pitman-Yor [75]).
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Some asymptotic laws for multidimensional BM. In: Aspects of Brownian Motion. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49966-4_7
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DOI: https://doi.org/10.1007/978-3-540-49966-4_7
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