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\iteman{io-port 00027220}
\itemau{Kalpazidou, Sophia}
\itemti{Continuous parameter circuit processes with finite state space.}
\itemso{Stochastic Processes Appl. 39, No.2, 301-323 (1991).}
\itemab
Summary: Given a finite set $S$, a class ${\cal C}$ of overlapping directed circuits in $S$ and a collection of weight functions $w\sb c: [0,+\infty)\to[0,+\infty)$, $c\in{\cal C}$, that verify certain topological and algebraic relations, we uniquely define a continuous parameter Markov process $(\xi\sb t)\sb{t\ge 0}$ called a circuit process. The constructive solution to a correspondence $(\xi\sb t)\sb{t\ge 0}\to\{{\cal C},w\sb c\}$, which becomes one-to-one when $\{{\cal C},w\sb c\}$ can be given a probabilistic interpretation, is described. In particular we show that the L\'evy-Austin-Ornstein theorem concerning the positiveness of the transition probabilities $p\sb{ij}(\cdot)$ is a qualitative property. Also it is proved that the intensities $q\sb{ij}$ have a probabilistic interpretation in terms of the sample paths of the discrete skeletons. Finally, analytical properties of the weight functions are studied.
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\itemut{analytical properties of the weight functions; Markov jump processes; mean number of cycles; discrete skeletons}
\itemli{doi:10.1016/0304-4149(91)90085-Q}
\end