Eventual Intersection for Sequences of Lévy Processes
نویسندگان
چکیده
[email protected] [email protected] Abstract: Consider the events fFn \ Sn 1 k=1 Fk = ;g, n 2 N, where (Fn) 1 n=1 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 in nitely often with positive probability if PfFi\Fj 6= ; jFjg > 0 a.s. for i 6= j. We present a counterexample to show that this condition is not su cient, and give one that is. The su cient condition always holds when Fn = fX t : 0 t Tg is the range of a L evy process X on the d-dimensional torus with uniformly distributed initial position and Pf90 s; t T : X i s = X j t g > 0 for i 6= j. We also establish an analogous result for the sequence of graphs f(t;X t ) : 0 t Tg.
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Additive functionals of several Lévy processes and self-intersection local times
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