Geodesic
Remark on locally constant self-similar processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 88-92

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Let $X=\{X(t),\ t\in\mathbb R_+\}$ be a self-similar process with index $\alpha>0$. We show that if $X$ is locally constant, and if $\mathbf P\{X(1)=0\}=0$, then the law of $X(t)$ is absolutely continuous. The applications of this result to homogeneous functionals of a multi-dimensional fractional Brownian motion are discussed. 
@article{ZNSL_2011_396_a4,
     author = {Yu. A. Davydov},
     title = {Remark on locally constant self-similar processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {88--92},
     publisher = {mathdoc},
     volume = {396},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a4/}
}
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Yu. A. Davydov. Remark on locally constant self-similar processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 88-92. http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a4/