ON THE MARKOV PROPERTY OF THE OCCUPATION TIME FOR CONTINUOUS-TIME INHOMOGENEOUS MARKOV CHAINS

摘要

It is known that the occupation time random field for a homogeneous Markov chain has the Markov property. We study the possibility of generalizing this result for inhomogeneous chains. Consider a process that is a homogeneous Markov chain with transition probability density Q_1 up to time T and with density Q_2 after T, where Q_1 ≠ Q_2. It turns out that even in this simplest case, the occupation time does not have the Markov property. Bibliography: 9 titles.