Persistence probabilities of mixed FBM and other mixed processes
Frank Aurzada,
Martin Kilian,
Ercan Sönmez
Abstract:We consider the sum of two self-similar centred Gaussian processes with different self-similarity indices. Under non-negativity assumptions of covariance functions and some further minor conditions, we show that the asymptotic behaviour of the persistence probability of the sum is the same as for the single process with the greater selfsimilarity index.In particular, this covers the mixed fractional Brownian motion introduced in [13] and shows that the corresponding persistence probability decays asymptoticall… Show more
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