XV: 01, 1-5, LNM 850 (1981)
FERNIQUE, Xavier
Sur les lois de certaines intégrales associées à des mouvements browniens (
Brownian motion)
Let $(Z_n)$ be a sequence of independent standard Brownian motions. Define by induction a sequence of processes $U_k$ by $U_0=Z_0$, $U_k(t)=\int_0^tU_{k-1}(s)dZ_k(s)$. Let $g_k(x)$ be the density of the random variable $U_k(1)$. Then the decrease at infinity of $g_k(x)$ is of the order $\exp(-C|x|^{\alpha})$ with $\alpha=2/(k+1)$ (slightly incorrect statement, see the paper for details)
Keywords: Iterated stochastic integralsNature: Original
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