2012/10/05 by Stella Brassesco, Brassesco, Stella, Silvana C. García Pire +1
Economics, Econometrics and Finance · Mathematics · #Analytic Number Theory Research #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:58J65 #msc:60J60 #msc:60J65
paper · pdf · doi:10.48550/arxiv.1210.1809
17 pages
arxiv created 2012/10/05 · arxiv updated 2012/10/08
We obtain a formula for the density of the winding number of planar Brownian motion around the origin, and deduce from it asymptotic expansions in inverse powers of the logarithm of the squared time, explicit in the angular variable. In particular, we obtain the corrections of any order to the Spitzer's law, and also to a local limit theorem for the windings.