A class of self-similar random measure
| Autor: | David Vere-Jones |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Statistics and Probability
Pure mathematics Class (set theory) Applied Mathematics 010102 general mathematics Self-similar process Poisson distribution Lévy process 01 natural sciences Point process Combinatorics Random measure symbols.namesake 010104 statistics & probability Moment measure symbols Product topology 0101 mathematics Mathematics |
| Zdroj: | Advances in Applied Probability. 37:908-914 |
| ISSN: | 1475-6064 0001-8678 |
| DOI: | 10.1017/s0001867800000598 |
| Popis: | We describe a class of self-similar random measure that generalizes the class of stable, completely random measure, or, in one dimension, the class of processes with stable independent increments. As with the stable processes, the realizations are purely atomic, but the masses of the atoms are not necessarily independent, but rather characterized by self-similar dependence relations. Indeed, the class can be described most effectively in terms of the point process on the product space for the locations and sizes (‘marksȉ) of the atoms. Then self-similarity reduces to an invariance relation (‘biscale invariance’) on the distribution of this marked point process. The condition can be satisfied when the marked point process is compound Poisson, corresponding to the nonnegative stable processes, but is by no means restricted to this case. An example is given which modifies and extends Ogata's epidemic-type aftershock sequence model for earthquake occurrence. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|