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Étude de processus généralisant l'Aire de Lévy
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  • Published: September 1986

Étude de processus généralisant l'Aire de Lévy

  • R. Berthuet1 

Probability Theory and Related Fields volume 73, pages 463–480 (1986)Cite this article

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Summary

Given ann-dimensional Brownian motionB(t)=(B 1(t), ...,B n (t)), we consider the stochastic process “n-dimensional Lévy's Stochastic Area”

$$L_n (t) = \sum\limits_\sigma {\varepsilon _\sigma \int\limits_0^t \ldots \int\limits_0^{t_2 } {B_{\sigma (1)} (t_1 )dB_{\sigma (2)} (t_1 ) \ldots dB_{\sigma (n)} (t_{n - 1} )} } $$

were ε(δ)) is the signature of the permutation δ.

We show that this process can be explicitly expressed, as a functionalF of 2-dimensional (ordinary) Lévy's Stochastic Areas.

F is calculated then evaluation of the characteristic function ofL 3 (t) follows.

Then an iterated logarithm theorem is proved for (L n (t)).

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Authors and Affiliations

  1. Département de Mathématiques Appliquées, Université de Clermont II, B.P. 45, F-63170, Aubiere, France

    R. Berthuet

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  1. R. Berthuet
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Berthuet, R. Étude de processus généralisant l'Aire de Lévy. Probab. Th. Rel. Fields 73, 463–480 (1986). https://doi.org/10.1007/BF00776243

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  • Received: 29 September 1985

  • Issue Date: September 1986

  • DOI: https://doi.org/10.1007/BF00776243

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