Integral representation of random variables with respect to Gaussian processes

Lauri Viitasaari*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

It was shown in Mishura etal. (Stochastic Process. AppL 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to cover a wide class of Gaussian processes. In particular, we consider a wide class of processes that are Holder continuous of order alpha > 1/2 and show that only local properties of the covariance function play role for such results.

Original languageEnglish
Pages (from-to)376-395
Number of pages20
JournalBernoulli
Volume22
Issue number1
DOIs
Publication statusPublished - Feb 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Follmer integral
  • Gaussian processes
  • generalised Lebesgue Stieltjes integral
  • integral representation
  • SMALL BALL PROBABILITIES

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