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Title: Regime switching processes and their long time behaviors Authors:  Abhishek Pal Majumder - University of Reading (United Kingdom) [presenting]
Abstract: Regime-switching processes have proved to be indispensable in the modeling of various phenomena in econometrics and physical science, allowing model parameters that traditionally were considered to be constant to fluctuate in a Markovian manner in line with empirical findings. We study diffusion processes of the Ornstein-Uhlenbeck type where the drift and diffusion coefficients are functions of an underlying Markov process with a stationary distribution on a countable state space. The exact long-time behavior of the process is determined for the three regimes corresponding to the expected drift strictly greater, equal or strictly less than zero, respectively. The time asymptotic behaviors are naturally expressed in terms of solutions to the well-studied distributional affine fixed-point equation $X=AX+B$ in law, where $X$ is independent of $(A,B)$. Additional applications will be discussed with findings in terms of Cox-Ingersoll-Ross diffusion, Geometric Brownian motions under Markovian and semi-Markovian environments. Long-term behaviors change in the transient cases for semi-Markov switching due to the difference in the tail behaviors of the sojourn times. Diffusion processes of Ornstein-Uhlenbeck types are continuous versions of the well-known auto-regressive processes so that the results can be translated for discrete time series as well.