We establish an exact formula relating the survival probability for certain
L\'evy flights (viz. asymmetric α-stable processes where α=1/2)
with the survival probability for the order statistics of the running maxima of
two independent Brownian particles. This formula allows us to show that the
persistence exponent δ in the latter, non Markovian case is simply
related to the persistence exponent θ in the former, Markovian case via:
δ=θ/2. Thus, our formula reveals a link between two recently
explored families of anomalous exponents: one exhibiting continuous deviations
from Sparre-Andersen universality in a Markovian context, and one describing
the slow kinetics of the non Markovian process corresponding to the difference
between two independent Brownian maxima.Comment: Accepted in EP