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Convergence to the maximum process of a fractional Brownian motion with shot noise

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  • Wang, Yizao

Abstract

We consider the maximum process of a random walk with additive independent noise in the form of maxi=1,…,n(Si+Yi). The random walk may have dependent increments, but its sample path is assumed to converge weakly to a fractional Brownian motion. When the largest noise has the same order as the maximal displacement of the random walk, we establish an invariance principle for the maximum process in the Skorohod topology. The limiting process is the maximum process of the fractional Brownian notion with shot noise generated by Poisson point processes.

Suggested Citation

  • Wang, Yizao, 2014. "Convergence to the maximum process of a fractional Brownian motion with shot noise," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 33-41.
    • Handle: RePEc:eee:stapro:v:90:y:2014:i:c:p:33-41
    DOI: 10.1016/j.spl.2014.03.014
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    References listed on IDEAS

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    1. Dehling, Herold & Durieu, Olivier & Volny, Dalibor, 2009. "New techniques for empirical processes of dependent data," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3699-3718, October.
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