A note on stability in distribution of Markov-modulated stochastic differential equations with reflection

We extend the stability criterion in distribution as in Yuan and Mao [C. Yuan and X. Mao. Asymptotic stability in distribution of stochastic differential equations with Markovian switching, Stochastic Process. Appl. 103 (2003) 277–291] to multi-dimensional reflected Markov-modulated stochastic differential equations on a closed positive orthant.