Approximation of fractional Brownian sheet by a random walk in anisotropic Besov space

N'zi, Modeste; Mendy, Ibrahima

doi:10.1515/rose.2007.009

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2009

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“…Some types of approximations of fractional Brownian sheets have been obtained recently (e.g. [2], [3], [9], [13], [14], [15]). In this paper we give a new type of approximation for certain values of the parameters by means of occupation time fluctuations of a stochastic particle model.…”

Section: Introductionmentioning

confidence: 99%

Convergence to weighted fractional Brownian sheets

Garzón¹

2009

COSA

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We define weighted fractional Brownian sheets, which are a class of Gaussian random fields with four parameters that include fractional Brownian sheets as special cases, and we give some of their properties. We show that for certain values of the parameters the weighted fractional Brownian sheets are obtained as limits in law of occupation time fluctuations of a stochastic particle model. In contrast with some known approximations of fractional Brownian sheets which use a kernel in a Volterra type integral representation of fractional Brownian motion with respect to ordinary Brownian motion, our approximation does not make use of a kernel.2000 Mathematics Subject Classification. Primary 60G60; Secondary 60G15, 60F05. Key words and phrases. Fractional Brownian sheet, weighted fractional Brownian sheet, approximation in law, long-range dependence.

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Section: Introductionmentioning

confidence: 99%

Convergence to weighted fractional Brownian sheets

Garzón¹

2009

COSA

View full text Add to dashboard Cite

show abstract

Approximation of fractional Brownian sheet by a random walk in anisotropic Besov space

Cited by 1 publication

References 4 publications

Convergence to weighted fractional Brownian sheets

Convergence to weighted fractional Brownian sheets

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