Local times and sample path properties of the Rosenblatt process

George Kerchev, Ivan Nourdin, Eero Saksman, Lauri Viitasaari

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Let Z=(Zt)t≥0 be the Rosenblatt process with Hurst index H∈(1∕2,1). We prove joint continuity for the local time of Z, and establish Hölder conditions for the local time. These results are then used to study the irregularity of the sample paths of Z. Based on analogy with similar known results in the case of fractional Brownian motion, we believe our results are sharp. A main ingredient of our proof is a rather delicate spectral analysis of arbitrary linear combinations of integral operators, which arise from the representation of the Rosenblatt process as an element in the second chaos.
Original languageEnglish
Pages (from-to)498-522
Number of pages25
JournalStochastic Processes and their Applications
Volume131
Early online date13 Oct 2020
DOIs
Publication statusPublished - Jan 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • Rosenblatt process
  • Local times
  • Fourier transform
  • Hilbert–Schmidt operator

Fingerprint Dive into the research topics of 'Local times and sample path properties of the Rosenblatt process'. Together they form a unique fingerprint.

Cite this