Abstract
Let B1, B2, ..., Bk be k independent Brownian motions with values in IRd. We study the long time asymptotics of additive functionals of the type:
where f is an integrable function on IRd. The critical cases are d = 2k−1 and d = 2k. We obtain results of the first order and of the second order (corresponding to
, which generalize classical results of Kallianpur-Robbins, Papanicolaou-Stroock-Varadhan, and Kasahara-Kotani, for k = 1, as well as recent results of Le Gall and Weinryb-Yor, for k = 2.
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Biane, P. (1989). Comportement asymptotique de certaines fonctionnelles additives de plusieurs mouvements browniens. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXIII. Lecture Notes in Mathematics, vol 1372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083974
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DOI: https://doi.org/10.1007/BFb0083974
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