A remark on positive sojourn times of symmetric processes
Résumé
We show that under some slight assumptions, the positive sojourn time of a product of symmetric processes converges towards ½ as the number of processes increases. Monotony properties are then exhibited in the case of symmetric stable processes, and used, via a recurrence relation, to obtain upper and lower bounds on the moments of the occupation time (in the first and third quadrants) for two-dimensional Brownian motion. Explicit values are also given for the second and third moments in the n-dimensional Brownian case.
Domaines
Probabilités [math.PR]
Fichier principal
SojournSym2.pdf (175.46 Ko)
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Fig2Col.eps (37.31 Ko)
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