# Rate of Strong Convergence to Markov-modulated Brownian motion.

@inproceedings{Nguyen2019RateOS, title={Rate of Strong Convergence to Markov-modulated Brownian motion.}, author={Giang T. Nguyen and Oscar Peralta}, year={2019} }

In Latouche and Nguyen (2015), the authors constructed a sequence of stochastic fluid processes and showed that it converges weakly to a Markov-modulated Brownian motion (MMBM). Here, we construct a different sequence of stochastic fluid processes and show that it converges strongly to an MMBM. To the best of our knowledge, this is the first result on strong convergence to a Markov-modulated Brownian motion.
We also prove that the rate of this almost sure convergence is $o(n^{-1/2} \log n… CONTINUE READING

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