A class of fractional Ornstein–Uhlenbeck processes mixed with a Gamma distribution
We consider a sequence of fractional Ornstein–Uhlenbeck processes, that are defined as solutions of a family of stochastic Volterra equations with a kernel given by the Riesz derivative kernel, and leading coefficients given by a sequence of independent Gamma random variables. We construct a new pro...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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VTeX
2022-11-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://www.vmsta.org/doi/10.15559/22-VMSTA216 |
| _version_ | 1797953890847555584 |
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| author | Luigi Amedeo Bianchi Stefano Bonaccorsi Luciano Tubaro |
| author_facet | Luigi Amedeo Bianchi Stefano Bonaccorsi Luciano Tubaro |
| author_sort | Luigi Amedeo Bianchi |
| collection | DOAJ |
| description | We consider a sequence of fractional Ornstein–Uhlenbeck processes, that are defined as solutions of a family of stochastic Volterra equations with a kernel given by the Riesz derivative kernel, and leading coefficients given by a sequence of independent Gamma random variables. We construct a new process by taking the empirical mean of this sequence. In our framework, the processes involved are not Markovian, hence the analysis of their asymptotic behaviour requires some ad hoc construction. In our main result, we prove the almost sure convergence in the space of trajectories of the empirical means to a given Gaussian process, which we characterize completely. |
| first_indexed | 2024-04-10T23:09:09Z |
| format | Article |
| id | doaj.art-976d19360d704720a698316fd164a4e6 |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-04-10T23:09:09Z |
| publishDate | 2022-11-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-976d19360d704720a698316fd164a4e62023-01-13T06:38:05ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542022-11-01101375710.15559/22-VMSTA216A class of fractional Ornstein–Uhlenbeck processes mixed with a Gamma distributionLuigi Amedeo Bianchi0Stefano Bonaccorsi1Luciano Tubaro2Università degli Studi di Trento, Via Sommarive 14, 38123 Povo (Trento), ItalyUniversità degli Studi di Trento, Via Sommarive 14, 38123 Povo (Trento), ItalyUniversità degli Studi di Trento, Via Sommarive 14, 38123 Povo (Trento), ItalyWe consider a sequence of fractional Ornstein–Uhlenbeck processes, that are defined as solutions of a family of stochastic Volterra equations with a kernel given by the Riesz derivative kernel, and leading coefficients given by a sequence of independent Gamma random variables. We construct a new process by taking the empirical mean of this sequence. In our framework, the processes involved are not Markovian, hence the analysis of their asymptotic behaviour requires some ad hoc construction. In our main result, we prove the almost sure convergence in the space of trajectories of the empirical means to a given Gaussian process, which we characterize completely.https://www.vmsta.org/doi/10.15559/22-VMSTA216Fractional Ornstein–Uhlenbeck processesempirical meansGamma mixingstochastic Volterra equationsgeneralized Wright function60G22 |
| spellingShingle | Luigi Amedeo Bianchi Stefano Bonaccorsi Luciano Tubaro A class of fractional Ornstein–Uhlenbeck processes mixed with a Gamma distribution Modern Stochastics: Theory and Applications Fractional Ornstein–Uhlenbeck processes empirical means Gamma mixing stochastic Volterra equations generalized Wright function 60G22 |
| title | A class of fractional Ornstein–Uhlenbeck processes mixed with a Gamma distribution |
| title_full | A class of fractional Ornstein–Uhlenbeck processes mixed with a Gamma distribution |
| title_fullStr | A class of fractional Ornstein–Uhlenbeck processes mixed with a Gamma distribution |
| title_full_unstemmed | A class of fractional Ornstein–Uhlenbeck processes mixed with a Gamma distribution |
| title_short | A class of fractional Ornstein–Uhlenbeck processes mixed with a Gamma distribution |
| title_sort | class of fractional ornstein uhlenbeck processes mixed with a gamma distribution |
| topic | Fractional Ornstein–Uhlenbeck processes empirical means Gamma mixing stochastic Volterra equations generalized Wright function 60G22 |
| url | https://www.vmsta.org/doi/10.15559/22-VMSTA216 |
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