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Estimation of the stability and the self-similarity indices through negative power variations

Abstract : This work is concerned with the estimation of the self-similarity and the stability indices of a H-self-similarity stable process (field) or a multifractional stable process.More precisely, let X be a H-sssi (self-similar stationary increments) symmetric alpha-stable process (field) or a multifractional stable process. We observe X at points k/n, k=0,...,n.Our estimates are based on beta-negative power variations with -1/2
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Thi To Nhu Dang. Estimation of the stability and the self-similarity indices through negative power variations. Complex Variables [math.CV]. Université Grenoble Alpes, 2016. English. ⟨NNT : 2016GREAM033⟩. ⟨tel-01679327⟩

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