Abstract
We characterize the class of exchangeable Feller processes evolving on partitions with boundedly many blocks. In continuous-time, the jump measure decomposes into two parts: a σ-finite measure on stochastic matrices and a collection of nonnegative real constants. This decomposition prompts a Lévy-Itô representation. In discrete-time, the evolution is described more simply by a product of independent, identically distributed random matrices.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1952-1979 |
| Number of pages | 28 |
| Journal | Annals of Probability |
| Volume | 42 |
| Issue number | 5 |
| DOIs | |
| State | Published - Sep 2014 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
Keywords
- Coalescent process
- De Finettis theorem
- Exchangeable random partition
- Feller process
- Interacting particle system
- Lévy-Ito̧ decomposition
- Paintbox process
- Random matrix product