Journal article
Central limit theorem for the size of the range of a renewal process
Statistics & probability letters, v 72(3), pp 249-264
2005
Abstract
We study the range of a Markov chain moving forward on the positive integers. For every position, there is a probability distribution on the size of the next forward jump. Taking a scaling limit as the means and variances of these distributions approach given continuous functions of position, there is a Gaussian limit law for the number of sites hit in a given rescaled interval.
We then apply this to random coupling. At each time,
n, a random function
f
n
is applied to the set
{
1
,
…
,
N
}
. The range
R
n
of the composition
f
n
∘
⋯
∘
f
1
shrinks as
n increases. A Gaussian limit law for the total number of values of
|
R
n
|
follows from the limit law together with an extension to non-compact rescaled ranges.
Metrics
Details
- Title
- Central limit theorem for the size of the range of a renewal process
- Creators
- Paweł Hitczenko - Drexel UniversityRobin Pemantle - University of Pennsylvania
- Publication Details
- Statistics & probability letters, v 72(3), pp 249-264
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000228541300007
- Scopus ID
- 2-s2.0-15844414497
- Other Identifier
- 991019167887904721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Statistics & Probability