Geodesic
Random walk and Wiener process in the neighbourhood of maximum
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 785-788
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We prove that suitably shifted and normed parts of the trajectory of Brownian motion situated to the left and to the right from the point of maximum are independent realisations of a Brownian bend. 
@article{TVP_1983_28_4_a17,
     author = {I. V. Denisov},
     title = {Random walk and {Wiener} process in the neighbourhood of maximum},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {785--788},
     year = {1983},
     volume = {28},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a17/}
}
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I. V. Denisov. Random walk and Wiener process in the neighbourhood of maximum. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 785-788. http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a17/