In this paper we prove two main results. The rst one is to prove the regularity of fractional derivatives of local time of symmetric stable process with index 1 < ≤ 2. Our result is similar to that of Marcus and Rosen in 1992 for local time. The second result is to give a ( , )-variation of fractional derivatives of local time of symmetric stable process with index 1 < ≤ 2. Our approach is similar to that of Eisenbaum in 2000 for local time.
In this paper, we give some regularities and limit theorems of some additive functionals of symmetric stable process of index 1 < a a 2 in some anisotropic Besov spaces.
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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