Integral representation of random variables with respect to Gaussian processes

Lauri Viitasaari

doi:10.3150/14-BEJ662

Integral representation of random variables with respect to Gaussian processes

Lauri Viitasaari^*

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-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 language	English
Pages (from-to)	376-395
Number of pages	20
Journal	Bernoulli
Volume	22
Issue number	1
DOIs	https://doi.org/10.3150/14-BEJ662
Publication status	Published - Feb 2016
MoE publication type	A1 Journal article-refereed

Keywords

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

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10.3150/14-BEJ662

https://projecteuclid.org/journals/bernoulli/volume-22/issue-1/Integral-representation-of-random-variables-with-respect-to-Gaussian-processes/10.3150/14-BEJ662.full

Cite this

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title = "Integral representation of random variables with respect to Gaussian processes",

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.",

keywords = "Follmer integral, Gaussian processes, generalised Lebesgue Stieltjes integral, integral representation, SMALL BALL PROBABILITIES",

author = "Lauri Viitasaari",

year = "2016",

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AB - 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.

KW - Follmer integral

KW - Gaussian processes

KW - generalised Lebesgue Stieltjes integral

KW - integral representation

KW - SMALL BALL PROBABILITIES

U2 - 10.3150/14-BEJ662

DO - 10.3150/14-BEJ662

M3 - Article

SN - 1350-7265

VL - 22

SP - 376

EP - 395

JO - Bernoulli

JF - Bernoulli

IS - 1

ER -

Integral representation of random variables with respect to Gaussian processes

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Keywords

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