Parameter Estimation for H-self-similar Stable Fields
Keywords:H-sssi fields, stable fields, self-similarity parameter estimator, stability parameter estimator, negative power variations
In this work, we are interested in -sssi - stable fields, that is, in stable random fields that are self-similar with parameter $H$ and have stationary increments. We give two estimators of the stability and the self-similar indices based on -negative power variations with The consistency of those two estimators are also proved. We illustrate these convergences with some examples: Levy fractional Brownian field, well-balanced linear fractional stable field and Takenaka random field.
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