TY - JOUR
T1 - Stationary flows and uniqueness of invariant measures
AU - Baccelli, François
AU - Konstantopoulos, Panagiotis Takis
PY - 2010
Y1 - 2010
N2 - We consider a quadruple (O, A, ?, µ), where A is a s-algebra of subsets of O, and ? is a measurable bijection from O into itself that preserves a finite measure µ.For each B ? A, we define and study the measure µB obtained by integrating on B the number of visits to a set of the trajectory of a point of O before returning to B. In particular, we obtain a generalization of Kac's formula and discuss its relation to discrete-time Palm theory. Although classical in appearance, its use in obtaining uniqueness of invariant measures of various stochastic models seems to be new. We apply the concept to countable Markov chains and Harris processes in general state space. © 2010 Brown University.
AB - We consider a quadruple (O, A, ?, µ), where A is a s-algebra of subsets of O, and ? is a measurable bijection from O into itself that preserves a finite measure µ.For each B ? A, we define and study the measure µB obtained by integrating on B the number of visits to a set of the trajectory of a point of O before returning to B. In particular, we obtain a generalization of Kac's formula and discuss its relation to discrete-time Palm theory. Although classical in appearance, its use in obtaining uniqueness of invariant measures of various stochastic models seems to be new. We apply the concept to countable Markov chains and Harris processes in general state space. © 2010 Brown University.
UR - http://www.scopus.com/inward/record.url?scp=77957367970&partnerID=8YFLogxK
M3 - Article
SN - 0033-569X
VL - 68
SP - 213
EP - 228
JO - Quarterly of Applied Mathematics
JF - Quarterly of Applied Mathematics
IS - 2
ER -