Pólya urns with immigration at random times
| Autor: | Nathan Ross, Adrian Röllin, Erol A. Peköz |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Random graph Discrete mathematics Degree (graph theory) 010102 general mathematics Asymptotic distribution Fixed point Preferential attachment 01 natural sciences Vertex (geometry) distributional convergence Pólya urns Combinatorics Moment (mathematics) distributional fixed point equation 010104 statistics & probability preferential attachment random graph Limit (mathematics) 0101 mathematics Mathematics |
| Zdroj: | Bernoulli 25, no. 1 (2019), 189-220 |
| Popis: | We study the number of white balls in a classical Polya urn model with the additional feature that, at random times, a black ball is added to the urn. The number of draws between these random times are i.i.d. and, under certain moment conditions on the inter-arrival distribution, we characterize the limiting distribution of the (properly scaled) number of white balls as the number of draws goes to infinity. The possible limiting distributions obtained in this way vary considerably depending on the inter-arrival distribution and are difficult to describe explicitly. However, we show that the limits are fixed points of certain probabilistic distributional transformations, and this fact provides a proof of convergence and leads to properties of the limits. The model can alternatively be viewed as a preferential attachment random graph model where added vertices initially have a random number of edges, and from this perspective, our results describe the limit of the degree of a fixed vertex. |
| Databáze: | OpenAIRE |
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