Two types of transitions can be found in the Markovian Arrival process or MAP: with and without arrivals. In transient transitions the chain jumps from one state to another with no arrival; in effective transitions, a single arrival occurs. We assume that in practice, only arrival times are...

The identification of different dynamics in sequential data has become an every day need in scientific fields such as marketing, bioinformatics, finance, or social sciences. Contrary to cross-sectional or static data, this type of observations (also known as stream data, temporal data,...

We study the problem of ergodicity, stationarity and maximum likelihood estimation for multinomial logistic models that include a latent process. Our work includes various models that have been proposed for the analysis of binary and, more general, categorical time series. We give verifiable...