The Hausdorff dimension of the range of the Lévy multistable processes

Ronan Le Guével (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We compute the Hausdorff dimension of the image X(E) of a non random Borel set E ⊂ [0, 1], where X is a Lévy multistable process in R. This extends the case where X is a classical stable Lévy process by letting the stability exponent α be a smooth function, which leads to non-homogeneous processes because their increments are not stationary and not necessarily independent. Contrary to the situation where the stability parameter is a constant, the dimension depends on the version of the multistable Lévy motion when the process has an infinite first moment.

Domaines: Probabilités [math.PR]

Ronan Le Guével. The Hausdorff dimension of the range of the Lévy multistable processes. Journal of Theoretical Probability, 2019, 32 (2), pp.765-780. ⟨10.1007/s10959-018-0847-8⟩. ⟨hal-01117357v2⟩