On the number of crossings of some levels by a sequence of diffusion processes
The limit behavior of the number of crossings of some sequence of levels by the following sequence of random variables $\xi_n(0)$, $\xi_n\left(\frac1{m}\right)$,..., $\xi_n\left(\frac{N}{m}\right)$, as the integers $n$, $m$, $N$ are increasing to infinity in some consistent way, is investigated, whe...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2013-01-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Online Access: | http://journals.pu.if.ua/index.php/cmp/article/view/30 |
| _version_ | 1819226425380569088 |
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| author | M. M. Osypchuk |
| author_facet | M. M. Osypchuk |
| author_sort | M. M. Osypchuk |
| collection | DOAJ |
| description | The limit behavior of the number of crossings of some sequence of levels by the following sequence of random variables $\xi_n(0)$, $\xi_n\left(\frac1{m}\right)$,..., $\xi_n\left(\frac{N}{m}\right)$, as the integers $n$, $m$, $N$ are increasing to infinity in some consistent way, is investigated, where $(\xi_n(t))_{t\ge0}$ for $n=1,2,\dots$ is a diffusion process on a real line $\mathbb{R}$ with its local characteristics (that is, drift and diffusion coefficients) $(a_n(x))_{x\in\mathbb{R}}$ and $(b_n(x))_{x\in\mathbb{R}}$ given by $a_n(x)=na(nx)$, $b_n(x)=b(nx)$ for $x\in\mathbb{R}$ and $n=1,2,\dots$ with some fixed functions $(a(x))_{x\in\mathbb{R}}$ and $(b(x))_{x\in\mathbb{R}}$. |
| first_indexed | 2024-12-23T10:25:17Z |
| format | Article |
| id | doaj.art-780ccf39a7634f7194ede10aca817722 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-12-23T10:25:17Z |
| publishDate | 2013-01-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-780ccf39a7634f7194ede10aca8177222022-12-21T17:50:35ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102013-01-011219119610.15330/cmp.1.2.191-19630On the number of crossings of some levels by a sequence of diffusion processesM. M. Osypchuk0Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineThe limit behavior of the number of crossings of some sequence of levels by the following sequence of random variables $\xi_n(0)$, $\xi_n\left(\frac1{m}\right)$,..., $\xi_n\left(\frac{N}{m}\right)$, as the integers $n$, $m$, $N$ are increasing to infinity in some consistent way, is investigated, where $(\xi_n(t))_{t\ge0}$ for $n=1,2,\dots$ is a diffusion process on a real line $\mathbb{R}$ with its local characteristics (that is, drift and diffusion coefficients) $(a_n(x))_{x\in\mathbb{R}}$ and $(b_n(x))_{x\in\mathbb{R}}$ given by $a_n(x)=na(nx)$, $b_n(x)=b(nx)$ for $x\in\mathbb{R}$ and $n=1,2,\dots$ with some fixed functions $(a(x))_{x\in\mathbb{R}}$ and $(b(x))_{x\in\mathbb{R}}$.http://journals.pu.if.ua/index.php/cmp/article/view/30 |
| spellingShingle | M. M. Osypchuk On the number of crossings of some levels by a sequence of diffusion processes Karpatsʹkì Matematičnì Publìkacìï |
| title | On the number of crossings of some levels by a sequence of diffusion processes |
| title_full | On the number of crossings of some levels by a sequence of diffusion processes |
| title_fullStr | On the number of crossings of some levels by a sequence of diffusion processes |
| title_full_unstemmed | On the number of crossings of some levels by a sequence of diffusion processes |
| title_short | On the number of crossings of some levels by a sequence of diffusion processes |
| title_sort | on the number of crossings of some levels by a sequence of diffusion processes |
| url | http://journals.pu.if.ua/index.php/cmp/article/view/30 |
| work_keys_str_mv | AT mmosypchuk onthenumberofcrossingsofsomelevelsbyasequenceofdiffusionprocesses |