Processes iterated ad libitum

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• 作者：Jé ; rô ; me Casse ; ^{jerome.casse@laposte.net" class="auth_mail" title="E-mail the corresponding author} ; Jean-Franç ; ois Marckert
• 关键词：primary ; 60J05 ; 60G52 ; 60J65 ; secondary ; 60G57 ; 60E99
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：126
• 期：11
• 页码：3353-3376
• 全文大小：538 K

文摘

Consider the n$n$th iterated Brownian motion I⁽ⁿ⁾=B_n∘⋯∘B₁$I^{\left(n\right)}=B_n\circ \cdots \circ B_1$. Curien and Konstantopoulos proved that for any distinct numbers t_i≠0$t_i\ne 0$, (I⁽ⁿ⁾(t₁),…,I⁽ⁿ⁾(t_k))$(I^{\left(n\right)}\left(t_1\right),\dots ,I^{\left(n\right)}\left(t_k\right))$ converges in distribution to a limit I[k]$I\left[k\right]$ independent of the t_i$t_i$’s, exchangeable, and gave some elements on the limit occupation measure of I⁽ⁿ⁾$I^{\left(n\right)}$. Here, we prove under some conditions, finite dimensional distributions of n$n$th iterated two-sided stable processes converge, and the same holds the reflected Brownian motions. We give a description of the law of I[k]$I\left[k\right]$, of the finite dimensional distributions of I⁽ⁿ⁾$I^{\left(n\right)}$, as well as those of the iterated reflected Brownian motion iterated ad libitum.