Fractal Transformation of Krein–Feller Operators
We consider a fractal transformed doubly reflected Brownian motion with state space being a Cantor-like set. By applying the theory of fractal transformations as developped by Barnsley, et al., together with an application of a generalised Taylor expression we show that its infinitesimal generator i...
Збережено в:
| Дата: | 2023 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
|
| Теми: | |
| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1017 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Репозитарії
Journal of Mathematical Physics, Analysis, Geometry| Резюме: | We consider a fractal transformed doubly reflected Brownian motion with state space being a Cantor-like set. By applying the theory of fractal transformations as developped by Barnsley, et al., together with an application of a generalised Taylor expression we show that its infinitesimal generator is given in terms of a second order measure geometric derivative $\frac{d}{d\mu}\frac{d}{d\mu}$ as introduced by Freiberg and Zähle. Furthermore we investigate its connection to the well known classical Krein-Feller operator $\frac{d}{d\mu}\frac{d}{dx}$ which is the generator of a so called “gap-diffusion”.
Mathematical Subject Classification 2020: 26A24, 26A30, 28A25, 28A80, 47A05, 60J35, 60J60 |
|---|