For the symbiotic branching model introduced in [
(2004) 127–160], it is shown that ageing and intermittency exhibit different behaviour for negative, zero, and positive correlations. Our approach also provides an alternative, elementary proof and refinements of classical results concerning second moments of the parabolic Anderson model with brownian potential. Some refinements to more general (also infinite range) kernels of recent ageing results of [
(2007) 461–480]...
We consider the one-sided exit problem – also called one-sided barrier problem – for (-fractionally) integrated random walks and Lévy processes. Our main result is that there exists a positive, non-increasing function such that the probability that any -fractionally integrated centered Lévy processes (or random walk) with some finite exponential moment stays below a fixed level until time behaves as for large . We also investigate when the fixed level can be replaced by a different barrier...
We investigate the small deviations under various norms for stable processes defined by the convolution of a smooth function with a real Lévy process. We show that the small ball exponent is uniquely determined by the norm and by the behaviour of at zero, which extends the results of
Lifshits and Simon,
(2005) 725–752
where this was proved for being a power function (Riemann-Liouville processes). In the Gaussian case, the same generality as Lifshits and Simon,
...
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