TY - JOUR
T1 - On the first exit time of a nonnegative markov process started at a quasistationary distribution
AU - Pollak, Moshe
AU - Tartakovsky, Alexander G.
PY - 2011/6
Y1 - 2011/6
N2 - Let {Mn}n≥0 be a nonnegative time-homogeneous Markov process. The quasistationary distributions referred to in this note are of the form QA(x) = limnn→∞ P(Mn ≤ x | M0 ≥ A, M1 ≥ A, . . . , Mn ≥ A). Suppose that M0 has distribution QA, and define T QAA = min{n | Mn > A, n ≥ 1}, the first time when Mn exceeds A. We provide sufficient conditions for QA(x) to be nonincreasing in A (for fixed x) and for TQAA to be stochastically nondecreasing in A.
AB - Let {Mn}n≥0 be a nonnegative time-homogeneous Markov process. The quasistationary distributions referred to in this note are of the form QA(x) = limnn→∞ P(Mn ≤ x | M0 ≥ A, M1 ≥ A, . . . , Mn ≥ A). Suppose that M0 has distribution QA, and define T QAA = min{n | Mn > A, n ≥ 1}, the first time when Mn exceeds A. We provide sufficient conditions for QA(x) to be nonincreasing in A (for fixed x) and for TQAA to be stochastically nondecreasing in A.
KW - Changepoint problem
KW - First exit time
KW - Markov process
KW - Quasistationary distribution
KW - Stationary distribution
UR - http://www.scopus.com/inward/record.url?scp=80054860775&partnerID=8YFLogxK
U2 - 10.1239/jap/1308662648
DO - 10.1239/jap/1308662648
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:80054860775
SN - 0021-9002
VL - 48
SP - 589
EP - 595
JO - Journal of Applied Probability
JF - Journal of Applied Probability
IS - 2
ER -