Asymptotic distribution of the derivative of the taut string accompanying Wiener process
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911297254195200 |
|---|---|
| author | Lifshits, Mikhail Podchishchailov, Andrei |
| author_facet | Lifshits, Mikhail Podchishchailov, Andrei |
| contents | In the article, we find the asymptotic distribution of the derivative of the taut string accompanying a Wiener process in a strip of fixed width on long time intervals. This enables to find explicit expressions for minimal energy (averaged function of the derivative) of an absolutely continuous function in this strip. For example, for kinetic energy which was considered earlier by Lifshits and Setterqvist, the minimal energy per unit of time tends to $π^2/6r^2$ where $r$ is the strip width. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04690 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic distribution of the derivative of the taut string accompanying Wiener process Lifshits, Mikhail Podchishchailov, Andrei Probability In the article, we find the asymptotic distribution of the derivative of the taut string accompanying a Wiener process in a strip of fixed width on long time intervals. This enables to find explicit expressions for minimal energy (averaged function of the derivative) of an absolutely continuous function in this strip. For example, for kinetic energy which was considered earlier by Lifshits and Setterqvist, the minimal energy per unit of time tends to $π^2/6r^2$ where $r$ is the strip width. |
| title | Asymptotic distribution of the derivative of the taut string accompanying Wiener process |
| topic | Probability |
| url | https://arxiv.org/abs/2411.04690 |