Loading…
On the First Exit Time of a Nonnegative Markov Process Started at a Quasistationary Distribution
Let { M n } n ≥0 be a nonnegative time-homogeneous Markov process. The quasistationary distributions referred to in this note are of the form Q A ( x ) = lim n →∞ P( M n ≤ x | M 0 ≤ A , M 1 ≤ A , …, M n ≤ A ). Suppose that M 0 has distribution Q A , and define T A Q A = min{ n | M n > A , n ≥ 1},...
Saved in:
| Published in: | Journal of applied probability 2011-06, Vol.48 (2), p.589-595 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Let {
M
n
}
n
≥0
be a nonnegative time-homogeneous Markov process. The quasistationary distributions referred to in this note are of the form
Q
A
(
x
) = lim
n
→∞
P(
M
n
≤
x
|
M
0
≤
A
,
M
1
≤
A
, …,
M
n
≤
A
). Suppose that
M
0
has distribution
Q
A
, and define
T
A
Q
A
= min{
n
|
M
n
>
A
,
n
≥ 1}, the first time when
M
n
exceeds
A
. We provide sufficient conditions for
Q
A
(
x
) to be nonincreasing in
A
(for fixed
x
) and for
T
A
Q
A
to be stochastically nondecreasing in
A
. |
|---|---|
| ISSN: | 0021-9002 1475-6072 |
| DOI: | 10.1017/S0021900200008081 |