This book explores regime-switching Brownian motion, a class of stochastic processes widely used in fields such as mathematical finance, risk theory, queueing theory, and epidemiological modeling. These processes are studied within the Markovian regime-switching framework, which captures dynamic environments characterized by shifts between different states or "regimes" for example, economic cycles, seasonal environmental variations, or short-term surges in activity.

The matrix-analytic approach, introduced approximately fifty years ago in the context of classical queueing theory,...