Flip-flop processes refer to a family of stochastic fluid which converge either standard Brownian motion (SBM) or Markov modulated (MMBM). In recent years, it has been shown that complex distributional aspects the univariate SBM and MMBM can be studied through limiting behavior flip-flop processes. Here, we construct two classes bivariate whose marginals strongly SBMs are dependent on each othe...

Abstract Latouche and Nguyen (2015b) constructed a sequence of stochastic fluid processes showed that it converges weakly to Markov-modulated Brownian motion (MMBM). Here, we construct different show strongly an MMBM. To the best our knowledge, this is first result on strong convergence motion. Besides implying weak convergence, such approximation constitutes powerful tool for developing deep r...