Approximation of heavy-tailed fractional Pearson diffusions in Skorokhod topology

Leonenko, Nikolai; Papić, Ivan; Sikorskii, Alla; Šuvak, Nenad

doi:10.1016/j.jmaa.2020.123934

Cited by 7 publications

(1 citation statement)

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“…Detailed discussion of such processes is also found in [4]. For a detailed study of the special class of heavy tailed processes, see [34,35,21]. An approach using subordination can be found in [4].…”

Section: Introductionmentioning

confidence: 99%

Stochastic analysis for vector-valued generalized grey Brownian motion

Böck¹,

Grothaus²,

Karlo³

2021

Preprint

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In this article, we show that the standard vector-valued generalization of a generalized grey Brownian motion (ggBm) has independent components if and only if it is a fractional Brownian motion. In order to extend ggBm with independent components, we introduce a vector-valued generalized grey Brownian motion (vggBm). The characteristic function of the corresponding measure is introduced as the product of the characteristic functions of the one-dimensional case. We show that for this measure, the Appell system and a calculus of generalized functions or distributions are accessible. We characterize these distributions with suitable transformations and give a d-dimensional Donsker's delta function as an example for such distributions. From there, we show the existence of local times and self-intersection local times of vggBm as distributions under some constraints, and compute their corresponding generalized expectations. At the end, we solve a system of linear SDEs driven by a vggBm noise in d dimensions.

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