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...
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| Datum: | 2023 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1017 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | 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 |
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