Limit theorems for iterated random topical operators
| dc.creator | Merlet, Glenn | |
| dc.date | 2005-03-28 | |
| dc.date | 2007-01-08 | |
| dc.date.accessioned | 2026-07-07T07:38:48Z | |
| dc.date.available | 2026-07-07T07:38:48Z | |
| dc.description | Let A(n) be a sequence of i.i.d. topical (i.e. isotone and additively homogeneous) operators. Let $x(n,x_0)$ be defined by $x(0,x_0)=x_0$ and $x(n,x_0)=A(n)x(n-1,x_0)$. This can modelize a wide range of systems including, task graphs, train networks, Job-Shop, timed digital circuits or parallel processing systems. When A(n) has the memory loss property, we use the spectral gap method to prove limit theorems for $x(n,x_0)$. Roughly speaking, we show that $x(n,x_0)$ behaves like a sum of i.i.d. real variables. Precisely, we show that with suitable additional conditions, it satisfies a central limit theorem with rate, a local limit theorem, a renewal theorem and a large deviations principle, and we give an algebraic condition to ensure the positivity of the variance in the CLT. When A(n) are defined by matrices in the \mp semi-ring, we give more effective statements and show that the additional conditions and the positivity of the variance in the CLT are generic. | |
| dc.identifier | https://arxiv.org/abs/math/0503634 | |
| dc.identifier | http://arxiv.org/abs/math/0503634 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121222 | |
| dc.subject | Probability | |
| dc.subject | Optimization and Control | |
| dc.subject | 60J05,60F05,90B,93C65;93B25 | |
| dc.title | Limit theorems for iterated random topical operators | |
| dc.type | text |