  The Bivariate Dynamic Contagion Processes (BDCP) are a broad class of
bivariate point processes characterized by the intensities as a general class
of piecewise deterministic Markov processes. The BDCP describes a rich dynamic
structure where the system is under the influence of both external and internal
factors modelled by a shot-noise Cox process and a generalized Hawkes process
respectively. In this paper we mainly address the stationarity issue for the
BDCP, which is important in applications. We investigate the stationary
distribution by applying the the Markov theory on the branching system
approximation representation of the BDCP. We find the condition under which
there exists a unique stationary distribution of the BDCP intensity and the
resulting BDCP has stationary increments. Moments of the stationary intensity
are provided by using the Markov property.
