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This note investigates the probability of non-crossing in squared Bessel processes, suggesting insights on crossing distribution.
In this note, we are interested in the probability that two independent squared Bessel processes do not cross for a long time. We show that this probability has a power decay which is given by the first zero of some hypergeometric function. We also compute along the way the distribution of the location where the crossing eventually occurs.
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Christophe Profeta (2025) studied this question.
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