Brownian semistationary processes and related processes

Orimar Sauri

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arXiv · 1710.05694

Brownian semistationary processes and related processes

Orimar Sauri

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Abstract

In this paper 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 $\varphi_{\alpha}\left(x\right)=L\left(x\right)x^{\alpha}$ 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 It\^o's formula for this subclass of $\mathcal{BSS}$ processes.

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Orimar Sauri. 2017-10-16. Brownian semistationary processes and related processes. https://arxiv.org/abs/1710.05694

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