Geodesic
Pathwise decompositions of~Brownian semistationary processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 1, pp. 98-125

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We find a pathwise decomposition of a certain class of Brownian semistationary processes ($\mathcal{BSS}$) in terms of fractional Brownian motions. To do this, we specialize in the case when the kernel of the $\mathcal{BSS}$ is given by $\varphi_{\alpha}(x)=L(x)x^{\alpha}$ with $\alpha\in(-1/2,0)\cup(0,1/2)$ and $L$ a continuous function slowly varying at zero. We use this decomposition to study some path properties and derive Itô's formula for this subclass of $\mathcal{BSS}$ processes.
Keywords: Brownian semistationary processes, fractional Brownian motion, stationary processes
Mots-clés : Volterra processes, Itô's formula. 
@article{TVP_2019_64_1_a5,
     author = {O. Sauri},
     title = {Pathwise decompositions {of~Brownian} semistationary processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {98--125},
     publisher = {mathdoc},
     volume = {64},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2019_64_1_a5/}
}
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O. Sauri. Pathwise decompositions of~Brownian semistationary processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 1, pp. 98-125. http://geodesic.mathdoc.fr/item/TVP_2019_64_1_a5/