Attraction to and repulsion from patches on the hypersphere and hyperplane for isotropic d-dimensional α-stable processes with index in α ∈ (0, 1] and d ≥ 2
Duration: 58 mins 56 secs
Share this media item:
Embed this media item:
Embed this media item:
About this item
| Description: |
Andreas Kyprianou (University of Bath)
22/04/2022 Programme: FD2W03 SemId: 35404 |
|---|
| Created: | 2022-05-02 02:04 |
|---|---|
| Collection: | Fractional differential equations |
| Publisher: | Andreas Kyprianou |
| Copyright: | Isaac Newton Institute |
| Language: | eng (English) |
| Abstract: | Consider a d-dimensional α-stable processes with index in α∈(0,1) and d≥2. Suppose that Ω is a region of the unit sphere S^{d−1} = {x ∈ R^d : |x| = 1}. We construct the aforesaid stable Lévy process conditioned to approach Ω continuously, either from inside S^{d−1}, from outside S^{d−1} or in an oscillatory way; all of which have zero probability. Our approach also extends to the setting of hitting bounded domains of (d-1)-dimensional hyperplanes. We appeal to a mixture of methods, appealing to the modern theory of self-similar Markov process as well as the classical potential analytic view. |
|---|---|
Available Formats
| Format | Quality | Bitrate | Size | |||
|---|---|---|---|---|---|---|
| MPEG-4 Video | 1280x720 | 746.48 kbits/sec | 322.21 MB | View | Download | |
| MPEG-4 Video | 640x360 | 237.22 kbits/sec | 102.40 MB | View | Download | |
| WebM | 1280x720 | 391.45 kbits/sec | 169.02 MB | View | Download | |
| WebM | 640x360 | 183.98 kbits/sec | 79.44 MB | View | Download | |
| iPod Video | 480x270 | 418.56 kbits/sec | 180.67 MB | View | Download | |
| MP3 | 44100 Hz | 249.77 kbits/sec | 107.93 MB | Listen | Download | |
| Auto * | (Allows browser to choose a format it supports) | |||||