Asymptotic Growth of Sample Paths of Tempered Fractional Brownian Motions, with Statistical Applications to Vasicek-Type Models
2024 (English)In: Fractal and Fractional, ISSN 2504-3110, Vol. 8, no 2, article id 79Article in journal (Refereed) Published
Abstract [en]
Tempered fractional Brownian motion (TFBM) and tempered fractional Brownian motion of the second kind (TFBMII) modify the power-law kernel in the moving average representation of fractional Brownian motion by introducing exponential tempering. We construct least-square estimators for the unknown drift parameters within Vasicek models that are driven by these processes. To demonstrate their strong consistency, we establish asymptotic bounds with probability 1 for the rate of growth of trajectories of tempered fractional processes.
Place, publisher, year, edition, pages
Multidisciplinary Digital Publishing Institute (MDPI) , 2024. Vol. 8, no 2, article id 79
Keywords [en]
asymptotic growth, fractional Brownian motion, parameter estimation, strong consistency, tempered fractional processes, Vasicek model
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-66279DOI: 10.3390/fractalfract8020079ISI: 001172079100001Scopus ID: 2-s2.0-85187282949OAI: oai:DiVA.org:mdh-66279DiVA, id: diva2:1845832
Note
Article; Export Date: 20 March 2024; Cited By: 0; Correspondence Address: K. Ralchenko; Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, 64/13 Volodymyrska St., 01601, Ukraine; email: kostiantynralchenko@knu.ua
2024-03-202024-03-202025-10-10Bibliographically approved