Displaying similar documents to “Some properties of exponential integrals of Levy processes and examples.”

Small deviations of iterated processes in the space of trajectories

Andrei Frolov (2013)

Open Mathematics

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We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes. When these conditions fail the asymptotics are quite different.

Asymptotic properties of power variations of Lévy processes

Jean Jacod (2007)

ESAIM: Probability and Statistics

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We determine the asymptotic behavior of the realized power variations, and more generally of sums of a given function  evaluated at the increments of a Lévy process between the successive times Δ for = 0,1,...,. One can elucidate completely the first order behavior, that is the convergence in probability of such sums, possibly after normalization and/or centering: it turns out that there is a rather wide variety of possible behaviors, depending on the structure of jumps and on the...