Systémy částic a prostorové procesy větvení
| Thesis title in Czech: | Systémy částic a prostorové procesy větvení |
|---|---|
| Thesis title in English: | Particle systems and spatial branching processes |
| Key words: | Systémy interagujících částic, proces větvení, rozklad pomocí kostry, dualita, intertwining, superproces. |
| English key words: | Interacting particle system, branching process, skeletal decomposition, duality, intertwining, superprocess. |
| Academic year of topic announcement: | 2015/2016 |
| Thesis type: | dissertation |
| Thesis language: | |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | Dr. Jan Swart |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 03.10.2016 |
| Date of assignment: | 03.10.2016 |
| Confirmed by Study dept. on: | 04.10.2016 |
| Guidelines |
| Systems of particles that are situated in space and multiply by branching will
be studied by a number of techniques, such as skeletal decomposition, intertwining, and duality. The starting point is a process with continuous-mass branching whose underlying motion is one-dimensional Brownian motion with drift towards and killing at the origin. Processes with other types of branching such as cooperative branching and processes with coalescence may also be studied. |
| References |
| J. Berestycki, N. Berestycki, and J. Schweinsberg. The genealogy of branching
Brownian motion with absorption. Ann. Probab. 41(2) (2013), 527–618. M. Eckhoff, A.E. Kyprianou, and M. Winkel. Spines, skeletons and the Strong Law of Large Numbers for superdiffusions. Ann. Probab. 43(5) (2015), 2545–2610. K. Fleischmann and J.M. Swart. Trimmed trees and embedded particle systems. Ann. Probab. 32(3A) (2004), 2179–2221. S.C. Harris, M. Hesse, and A.E. Kyprianou. Branching Brownian motion in a strip: survival near criticality. Ann. Probab. 44(1) (2016), 235–275. |