Continous random trees
| Autor: | Ganjour, Dmitri |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Rué Perna, Juan José |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Galton-Watson process
Kesten's tree Random trees Processos estocàstics Discrete trees 60 Probability theory and stochastic processes::60G Stochastic processes [Classificació AMS] Height process Continuous random trees Mathematics::Probability Stochastic processes Matemàtiques i estadística::Estadística matemàtica [Àrees temàtiques de la UPC] Brownian motion Local convergence of random trees Reflected Brownian motion |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Recercat. Dipósit de la Recerca de Catalunya instname |
| Popis: | The Brownian motion has played an important role in the development of probability theory and stochastic processes. We are going to see that it appears in the limiting process of several discrete processes. In particular, we will define discrete processes on Galton-Watson trees to see 2 different types of limits, which are the local limits and the scaling limits. The first result, Kesten's theorem, is a result for the local limits. We are going to look at the trees up to an arbitrary fixed height and therefore only consider what happens at a finite distance from the root. The second result concerns the limit of the rescaled height processes of an infinite Galton-Watson forest. We are going to consider sequences of trees where the branches are scaled by some factor so that all the vertices remain at finite distance from the root. Due to the scaling, the branches have infinitesimal length. These scaling limits lead to the so-called continuous random trees. Incoming |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|