Finite variation of fractional Levy processes

Christian Bender · Alexander Lindner · Markus Schicks

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Stochastic processes and financial applications Fractional Differential Equations Solutions Probability and Risk Models

Abstract

Various characterizations for fractional Levy process to be of finite variation are obtained, one of which is in terms of the characteristic triplet of the driving Levy process, while others are in terms of differentiability properties of the sample paths. A zero-one law and a formula for the expected total variation is also given.

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References

2008Stochastic Calculus for Fractional Brownian Motion and Related Processes 1997Stable Non-Gaussian Random ProcessesGennady Samorodnitsky and Murad S. Taqqu Chapman and Hall, 1994 2006Fractional Lévy processes with an application to long memory moving average processes 2000Identification and properties of real harmonizable fractional Levy motions 2009Lévy driven moving averages and semimartingales

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2011Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model 2017Power variation for a class of stationary increments Lévy driven moving averages

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