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XIV: 38, 343-346, LNM 784 (1980)
YOR, Marc
Remarques sur une formule de Paul Lévy (Brownian motion)
Given a two-dimensional Brownian motion $(X_t,Y_t)$, Lévy's area integral formula gives the characteristic function $E[\,\exp(iu\int_0^1 X_s\,dY_s-Y_s\,dX_s)\,\,|\,\, X_0=x, Y_0=y]$. A short proof of this formula is given, and it is shown how to deduce from it the apparently more general $E[\exp(iu\int_0^1 X_sdY_s+iv\int_0^1 Y_sdX_s)\,]$ computed by Berthuet
Keywords: Area integral formula
Nature: Original
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