Identification and properties of real harmonizable fractional Lévy motions
The authors construct a real harmonizable fractional Lévy motion (RHFLM) as a real-valued field \( X_H \) which admits the integral representation \[ X_H(x) = \int_{R^d}\frac{e^{ix\xi}-1}{\|\xi\|^{d/2 + H}}L(d\xi). \] Here \( L(d\xi) \) is the sum of a Wiener measure \( W(d\xi) \) and of an independent Lévy measure \( M(d\xi) \) the control measure of which (a) has moments of order \(p\), \(\forall p \geq 2\); (b) is rotationally invariant. The authors show that these fields are locally self-similar and the corresponding tangent field is an FBM. Furthermore, the sample paths of the RHFLM are a.s. Hölder-continuous with exponent \( H \). In the last section the fractional index \( H \) is estimated using a generalized quadratic variation.
scientific article; zbMATH DE number 1786695