Generalized Quadratic Variations of Gaussian Processes
Limit Theorems and Applications to Fractional Gaussian Processes
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This book is about "generalized quadratic variations of Gaussian processes". Generalized quadratic variations means that we consider mathematical objects wich are generalization of the classical quadratic variations used in semi-martingale theory. The Gaussian processes studied in this work are of fractional type, that is they resemble the fractional Brownian motion (FBM). In FBM theory, mathematicians consider second order quadratic variations which yield good estimation of the Hurst index of FBM. The aim of this work is to generalize this results to other fractional processes, without statio...
This book is about "generalized quadratic variations of Gaussian processes". Generalized quadratic variations means that we consider mathematical objects wich are generalization of the classical quadratic variations used in semi-martingale theory. The Gaussian processes studied in this work are of fractional type, that is they resemble the fractional Brownian motion (FBM). In FBM theory, mathematicians consider second order quadratic variations which yield good estimation of the Hurst index of FBM. The aim of this work is to generalize this results to other fractional processes, without stationarity or harmonizable representation assumptions.
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