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Abstract:
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Long Range Dependence (LRD) has been widely used to model Internet data traffic, volatility of stock prices in Finance, water levels of rivers, and many other phenomena of interest. In this talk, we will look at LRD in the multivariate context in the light of an important class of LRD-related models, called Operator Fractional Brownian Motions (OFBMs). These are Gaussian operator self-similar processes with stationary increments. They are multivariate analogues of the one-dimensional fractional Brownian motion. We establish integral representations of OFBMs, study their basic properties and examine questions of uniqueness. We also show the existence of a kind of rigidity, called Dichotomy Principle, in the spectrum of Operator Fractional Gaussian Noise, i.e., the increment process of an OFBM.
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