Strong convergence to two-dimensional alternating Brownian motion processes

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 other, as alternating two-dimensional While not Gaussian, they possess desirable qualities, such being tractable having time-varying correlation coefficient function.