On the cross-variation of a class of stochastic processes
The present paper deals with the study of the cross-variation of two-dimensional stochastic process defined using the Young integral with respect to a continuous, α-self-similar Gaussian process that does not necessarily have stationary increments, with increment exponent some β>0. We analyze the...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-11-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037424000797 |
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| author | Soufiane Moussaten |
| author_facet | Soufiane Moussaten |
| author_sort | Soufiane Moussaten |
| collection | DOAJ |
| description | The present paper deals with the study of the cross-variation of two-dimensional stochastic process defined using the Young integral with respect to a continuous, α-self-similar Gaussian process that does not necessarily have stationary increments, with increment exponent some β>0. We analyze the limit, in probability, of the so-called cross-variation when β in 0,2α, and we finish by providing some examples of known processes that satisfy the required assumptions. |
| format | Article |
| id | doaj-art-710f6b9ef05f43fcb23fcaac4e92ea4e |
| institution | DOAJ |
| issn | 2590-0374 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-710f6b9ef05f43fcb23fcaac4e92ea4e2025-08-20T02:49:29ZengElsevierResults in Applied Mathematics2590-03742024-11-012410050910.1016/j.rinam.2024.100509On the cross-variation of a class of stochastic processesSoufiane Moussaten0Department of Mathematics and Computer Science, Faculty of Science Aïn-Chock, Hassan II University, Casablanca, MoroccoThe present paper deals with the study of the cross-variation of two-dimensional stochastic process defined using the Young integral with respect to a continuous, α-self-similar Gaussian process that does not necessarily have stationary increments, with increment exponent some β>0. We analyze the limit, in probability, of the so-called cross-variation when β in 0,2α, and we finish by providing some examples of known processes that satisfy the required assumptions.http://www.sciencedirect.com/science/article/pii/S2590037424000797Gaussian processesSelf-similar stochastic processesYoung integralPower variationSubfractional brownian motionBifractional brownian motion |
| spellingShingle | Soufiane Moussaten On the cross-variation of a class of stochastic processes Results in Applied Mathematics Gaussian processes Self-similar stochastic processes Young integral Power variation Subfractional brownian motion Bifractional brownian motion |
| title | On the cross-variation of a class of stochastic processes |
| title_full | On the cross-variation of a class of stochastic processes |
| title_fullStr | On the cross-variation of a class of stochastic processes |
| title_full_unstemmed | On the cross-variation of a class of stochastic processes |
| title_short | On the cross-variation of a class of stochastic processes |
| title_sort | on the cross variation of a class of stochastic processes |
| topic | Gaussian processes Self-similar stochastic processes Young integral Power variation Subfractional brownian motion Bifractional brownian motion |
| url | http://www.sciencedirect.com/science/article/pii/S2590037424000797 |
| work_keys_str_mv | AT soufianemoussaten onthecrossvariationofaclassofstochasticprocesses |