## Abstract

n this paper, the authors study the regularity of sample paths of Volterra processes defined by

M(t)=∫t0F(t,r)dX(r),t∈R+,

where X is a semimartingale and F is a real-valued function. Under the regularity assumption that F(t,r) is a function of smooth variation of index d∈(0,1) (Definition 1.3), they derive the regularity of the increments of M (Theorem 1.4), which is very precise when X is discontinuous, and then they provide a uniform-in-time bound on the increments of M (Theorem 1.5). As an application, they obtain the optimal Hölder exponent for fractional Lévy processes (Definition 1.1), which improves a result of T. Marquardt

M(t)=∫t0F(t,r)dX(r),t∈R+,

where X is a semimartingale and F is a real-valued function. Under the regularity assumption that F(t,r) is a function of smooth variation of index d∈(0,1) (Definition 1.3), they derive the regularity of the increments of M (Theorem 1.4), which is very precise when X is discontinuous, and then they provide a uniform-in-time bound on the increments of M (Theorem 1.5). As an application, they obtain the optimal Hölder exponent for fractional Lévy processes (Definition 1.1), which improves a result of T. Marquardt

Original language | American English |
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Pages (from-to) | 359–377. |

Journal | Communications on Stochastic Analysis |

Volume | 6 |

Issue number | 3 |

State | Published - 2012 |