On integral representations of operator fractional Brownian fields

Changryong Baek; Gustavo Didier; Vladas Pipiras

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arXiv · 1403.6179

On integral representations of operator fractional Brownian fields

Changryong Baek·Gustavo Didier·Vladas Pipiras

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Abstract

Operator fractional Brownian fields (OFBFs) are Gaussian, stationary-increment vector random fields that satisfy the operator self-similarity relation {X(c^{E}t)}_{t in R^m} L= {c^{H}X(t)}_{t in R^m}. We establish a general harmonizable representation (Fourier domain stochastic integral) for OFBFs. Under additional assumptions, we also show how the harmonizable representation can be reexpressed as a moving average stochastic integral, thus answering an open problem described in Bierme et al.(2007), "Operator scaling stable random fields", Stochastic Processes and their Applications 117, 312--332.

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Changryong Baek, Gustavo Didier, Vladas Pipiras. 2014-05-23. On integral representations of operator fractional Brownian fields. https://arxiv.org/abs/1403.6179

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