Conditioning an additive functional of a Markov chain to stay nonnegative. I. Survival for a long time
2005 ◽
Vol 37
(4)
◽
pp. 1015-1034
◽
Keyword(s):
Let (Xt)t≥0 be a continuous-time irreducible Markov chain on a finite state space E, let v be a map v: E→ℝ\{0}, and let (φt)t≥0 be an additive functional defined by φt=∫0tv(Xs)d s. We consider the case in which the process (φt)t≥0 is oscillating and that in which (φt)t≥0 has a negative drift. In each of these cases, we condition the process (Xt,φt)t≥0 on the event that (φt)t≥0 is nonnegative until time T and prove weak convergence of the conditioned process as T→∞.
2005 ◽
Vol 37
(04)
◽
pp. 1015-1034
◽
Keyword(s):
2005 ◽
Vol 37
(4)
◽
pp. 1035-1055
◽
Keyword(s):
2005 ◽
Vol 37
(04)
◽
pp. 1035-1055
◽
Keyword(s):
1982 ◽
Vol 19
(02)
◽
pp. 272-288
◽
Keyword(s):
1993 ◽
Vol 113
(2)
◽
pp. 381-386
Keyword(s):
2014 ◽
Vol 51
(4)
◽
pp. 1114-1132
◽
2009 ◽
Vol 3
(3)
◽
pp. 1204-1231
◽
Keyword(s):
1990 ◽
Vol 22
(04)
◽
pp. 802-830
◽