Green Measures for a Class of non-Markov Processes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929300570112000 |
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| author | Suryawan, Herry Pribawanto da Silva, José Luís |
| author_facet | Suryawan, Herry Pribawanto da Silva, José Luís |
| contents | In this paper, we investigate the Green measure for a class of non-Gaussian processes in $\mathbb{R}^{d}$. These measures are associated with the family of generalized grey Brownian motions $B_{β,α}$, $0<β\le1$, $0<α\le2$. This family includes both fractional Brownian motion, Brownian motion, and other non-Gaussian processes. We show that the perpetual integral exists with probability $1$ for $dα>2$ and $1<α\le2$. The Green measure then generalizes those measures of all these classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02076 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Green Measures for a Class of non-Markov Processes Suryawan, Herry Pribawanto da Silva, José Luís Probability Functional Analysis 60G22, 60J45, 60K50 In this paper, we investigate the Green measure for a class of non-Gaussian processes in $\mathbb{R}^{d}$. These measures are associated with the family of generalized grey Brownian motions $B_{β,α}$, $0<β\le1$, $0<α\le2$. This family includes both fractional Brownian motion, Brownian motion, and other non-Gaussian processes. We show that the perpetual integral exists with probability $1$ for $dα>2$ and $1<α\le2$. The Green measure then generalizes those measures of all these classes. |
| title | Green Measures for a Class of non-Markov Processes |
| topic | Probability Functional Analysis 60G22, 60J45, 60K50 |
| url | https://arxiv.org/abs/2404.02076 |