We study the asymptotics, for small and large values, of the supremum of a product of symmetric stable processes. We show in particular that the lower tail exponent remains the same as for only one process, possibly up to some logarithmic terms. The proof relies on a path construction of stable bridges using last sign changes.
"On the supremum of products of symmetric stable processes." Electron. Commun. Probab. 23 1 - 13, 2018. https://doi.org/10.1214/18-ECP193