Particle picture representation of the non-symmetric Rosenblatt process and Hermite processes of any order

Łukasz Treszczotko

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arXiv · 1703.00781

Particle picture representation of the non-symmetric Rosenblatt process and Hermite processes of any order

Łukasz Treszczotko

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Abstract

We provide a particle picture representation for the non-symmetric Rosenblatt process and for Hermite processes of any order, extending the result of Bojdecki, Gorostiza and Talarczyk in~\cite{FILT}. We show that these processes can be obtained as limits in the sense of finite-dimensional distributions of certain functionals of a system of particles evolving according to symmetric stable L\'{e}vy motions. In the case of $k$-Hermite processes the corresponding functional involves $k$-intersection local time of symmetric stable L\'{e}vy processes

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Łukasz Treszczotko. 2017-03-02. Particle picture representation of the non-symmetric Rosenblatt process and Hermite processes of any order. https://arxiv.org/abs/1703.00781

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