Occupation time problem for multifractional Brownian motion

  1. Mohamed Ait Ouahra
  2. Raby Guerbaz
  3. Hanae Ouahhabi
  4. Aissa Sghir

Abstract

In this paper, by using a Fourier analytic approach, we investigate sample path properties of the fractional derivatives of multifractional Brownian motion local times. We also show that those additive functionals satisfy a property of local asymptotic self-similarity. As a consequence, we derive some local limit theorems for the occupation time of multifractional Brownian motion in the space of continuous functions.

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Probability and Mathematical Statistics

39, z. 1, 2019

Pages from 99 to 113

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