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- W2138762014 abstract "Consider the events ${F_n cap bigcup_{k=1}^{n-1} F_k = emptyset}$, $n in N$, where $(F_n)_{n=1}^infty$ is an i.i.d. sequence of stationary random subsets of a compact group $G$. A plausible conjecture is that these events will not occur infinitely often with positive probability if $P{F_i cap F_j ne emptyset mid F_j} gt 0$ a.s. for $i ne j$. We present a counterexample to show that this condition is not sufficient, and give one that is. The sufficient condition always holds when $F_n = {X_t^n : 0 le t le T}$ is the range of a Lévy process $X^n$ on the $d$-dimensional torus with uniformly distributed initial position and $P{exists 0 le s, t le T : X_s^i = X_t^j } gt 0$ for $i ne j$. We also establish an analogous result for the sequence of graphs ${(t,X_t^n) : 0 le t le T}$." @default.
- W2138762014 created "2016-06-24" @default.
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- W2138762014 date "1998-01-01" @default.
- W2138762014 modified "2023-09-26" @default.
- W2138762014 title "Eventual Intersection for Sequences of Lévy Processes" @default.
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- W2138762014 doi "https://doi.org/10.1214/ecp.v3-989" @default.
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