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Stochastic analysis for vector-valued generalized grey Brownian motion
Technische Universität Kaiserslautern, Germany.ORCID iD: 0000-0002-8400-0416
Technische Universität Kaiserslautern, Germany.
Technische Universität Kaiserslautern, Germany;Mindanao State University - Iligan Institute of Technology, Philippines.
2023 (English)In: Theory Probability and Mathematical Statistics, ISSN 0094-9000, no 108, p. 1-27Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2023. no 108, p. 1-27
National Category
Probability Theory and Statistics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-124515DOI: 10.1090/tpms/1184ISI: 000985914500001Scopus ID: 2-s2.0-85164407673OAI: oai:DiVA.org:lnu-124515DiVA, id: diva2:1802886
Available from: 2023-10-06 Created: 2023-10-06 Last updated: 2023-10-19Bibliographically approved

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Bock, Wolfgang

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