Name
Title | ||
|---|---|---|
Power-Law Distributions from Sigma-Pi Structure of Sums of Random Multiplicative Processes. |
Abstract | ||
|---|---|---|
We introduce a simple growth model in which the sizes of entities evolve as multiplicative random processes that start at different times. A novel aspect we examine is the dependence among entities. For this, we consider three classes of dependence between growth factors governing the evolution of sizes: independence, Kesten dependence and mixed dependence. We take the sum X of the sizes of the entities as the representative quantity of the system, which has the structure of a sum of product terms (Sigma-Pi), whose asymptotic distribution function has a power-law tail behavior. We present evidence that the dependence type does not alter the asymptotic power-law tail behavior, nor the value of the tail exponent. However, the structure of the large values of the sum X is found to vary with the dependence between the growth factors (and thus the entities). In particular, for the independence case, we find that the large values of X are contributed by a single maximum size entity: the asymptotic power-law tail is the result of such single contribution to the sum, with this maximum contributing entity changing stochastically with time and with realizations. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.3390/e19080417 | ENTROPY |
Keywords | Field | DocType |
power-law,random multiplicative process,stochastic process,growth model,dependence | Pi,Growth model,Exponent,Multiplicative function,Stochastic process,Sigma,Statistics,Power law,Mathematics,Asymptotic distribution | Journal |
Volume | Issue | ISSN |
19 | 8 | 1099-4300 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Arthur Matsuo Yamashita Rios de Sousa | 1 | 0 | 0.68 |
| Hideki Takayasu | 2 | 7 | 5.61 |
| Didier Sornette | 3 | 238 | 37.50 |
| Misako Takayasu | 4 | 18 | 5.72 |