Geodesic
On the large-deviation principle for the winding angle of a Brownian trajectory around the origin
Teoriâ slučajnyh processov, Tome 20 (2015) no. 2, pp. 63-84

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In this article we analyse the possibility of obtaining the large-deviation principle for the winding angle of a Brownian motion trajectory around the origin. We prove the weak large-deviation principle and show that the full large-deviation principle cannot hold with any rate function.
Keywords: Large deviations, windings, winding numbers, Brownian motion. 
@article{THSP_2015_20_2_a4,
     author = {V. A. Kuznetsov},
     title = {On the large-deviation principle for the winding angle of a {Brownian} trajectory around the origin},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {63--84},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2015_20_2_a4/}
}
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V. A. Kuznetsov. On the large-deviation principle for the winding angle of a Brownian trajectory around the origin. Teoriâ slučajnyh processov, Tome 20 (2015) no. 2, pp. 63-84. http://geodesic.mathdoc.fr/item/THSP_2015_20_2_a4/