Abstract
We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler distributions, both in the weak topology of distributions and a.s. in the space of distributions.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2448-2462 |
| Number of pages | 15 |
| Journal | Stochastic Processes and their Applications |
| Volume | 128 |
| Issue number | 7 |
| DOIs | |
| State | Published - Jul 1 2018 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics
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On the local times of stationary processes with conditional local limit theorems. / Denker, Manfred Heinz; Zheng, Xiaofei.
In: Stochastic Processes and their Applications, Vol. 128, No. 7, 01.07.2018, p. 2448-2462.Research output: Contribution to journal › Article
TY - JOUR
T1 - On the local times of stationary processes with conditional local limit theorems
AU - Denker, Manfred Heinz
AU - Zheng, Xiaofei
PY - 2018/7/1
Y1 - 2018/7/1
N2 - We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler distributions, both in the weak topology of distributions and a.s. in the space of distributions.
AB - We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler distributions, both in the weak topology of distributions and a.s. in the space of distributions.
UR - http://www.scopus.com/inward/record.url?scp=85030858462&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85030858462&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2017.09.012
DO - 10.1016/j.spa.2017.09.012
M3 - Article
AN - SCOPUS:85030858462
VL - 128
SP - 2448
EP - 2462
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 7
ER -