Nonstationary Markov processes in phase transition modelling

The geophysical and geological features of a seismic region determine the succession of the earthquake occurrences; we assume that their temporal variations produce state changes in the physical system. We model these temporal variations and, at the same time, the seismic sequence by a state-space model. A state-space model is composed by two stochastic processes respectively called state and observed process. The state process drives the state changes of the physical system, while the observed process models the sequence of the earthquakes all through the stay in each state. We choose the observed process to be a point process such that its risk function has a different expression for each state. In a previous preliminary study we defined the state process to be a homogeneous Markov process, that is the transition probabilities from a state to another were constant in time. In the present work, we consider the state process to be a non-homogeneous Markov process and we investigate how to define time-dependent transition probabilities by exploiting the available physical knowledge.