Example of a Gaussian self-similar field with stationary rectangular\n increments that is not a fractional Brownian sheet

2014/03/05 by Vitalii Makogin, Makogin, Vitalii, Yuliya Mishura +1 · 2 citations
Economics, Econometrics and Finance · Environmental Science · #60G18 #60G22 #60G60 #Analysis of environmental and stochastic processes #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1403.1215

openalex publication_date 2014/03/05 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We consider anisotropic self-similar random fields, in particular, the\nfractional Brownian sheet. This Gaussian field is an extension of fractional\nBrownian motion. We prove some properties of covariance function for\nself-similar fields with rectangular increments. Using Lamperti transformation\nwe obtain properties of covariance function for the corresponding stationary\nfields. We present an example of a Gaussian self-similar field with stationary\nrectangular increments that is not a fractional Brownian sheet.\n

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• Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration
• On the passage times of self-similar Gaussian processes on curved boundaries

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