Abstract
This chapter looks at Long Range Dependent models which are useful in modeling real world signals having outliers or long tailed statistical distributions. The concept of stable distribution is introduced and many standard distributions like symmetric \(\alpha\)stable, Gaussian, Cauchy, etc. are obtained from the generalized description of the family of stable distributions. Self-similarity for random processes is next introduced and the ideas of fractional Brownian motion, fractional and multi-fractional Gaussian noise, etc. are discussed in this context. The Hurst parameter which is a measure of self-similarity is discussed next and a few methods to estimate it are subsequently outlined.
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Das, S., Pan, I. (2012). Long Range Dependence, Stable Distributions and Self-Similarity. In: Fractional Order Signal Processing. SpringerBriefs in Applied Sciences and Technology(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23117-9_3
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DOI: https://doi.org/10.1007/978-3-642-23117-9_3
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