Geodesic
Singles in a Markov Chain
Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 27

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $\{X_i,i\geq 1\}$ denote a sequence of variables that take values in $\{0,1\}$ and suppose that the sequence forms a Markov chain with transition matrix $P$ and with initial distribution $(q,p)=(P(X_1=0),P(X_1=1))$. Several authors have studied the quantities $S_n$, $Y(r)$ and $AR(n)$, where $S_n=\sum_{i=1}^nX_i$ denotes the number of successes, where $Y(r)$ denotes the number of experiments up to the $r$-th success and where $AR(n)$ denotes the number of runs. In the present paper we study the number of singles $AS(n)$ in the vector $(X_1,X_2,\dots,X_n)$. A single in a sequence is an isolated value of $0$ or $1$, i.e., a run of length $1$. Among others we prove a central limit theorem for $AS(n)$.
DOI : 10.2298/PIM0897027O
Classification : 60J10 60F05, 60K99, 60J20 
@article{10_2298_PIM0897027O,
     author = {Edward Omey and Stefan Van Gulck},
     title = {Singles in a {Markov} {Chain}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {27 },
     publisher = {mathdoc},
     volume = {_N_S_83},
     number = {97},
     year = {2008},
     doi = {10.2298/PIM0897027O},
     zbl = {1199.60265},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0897027O/}
}
TY  - JOUR
AU  - Edward Omey
AU  - Stefan Van Gulck
TI  - Singles in a Markov Chain
JO  - Publications de l'Institut Mathématique
PY  - 2008
SP  - 27 
VL  - _N_S_83
IS  - 97
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM0897027O/
DO  - 10.2298/PIM0897027O
LA  - en
ID  - 10_2298_PIM0897027O
ER  - 
%0 Journal Article
%A Edward Omey
%A Stefan Van Gulck
%T Singles in a Markov Chain
%J Publications de l'Institut Mathématique
%D 2008
%P 27 
%V _N_S_83
%N 97
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM0897027O/
%R 10.2298/PIM0897027O
%G en
%F 10_2298_PIM0897027O
Edward Omey; Stefan Van Gulck. Singles in a Markov Chain. Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 27 . doi: 10.2298/PIM0897027O

Cité par Sources :