  This work develops Feynman-Kac formulas for a class of regime-switching jump
diffusion processes, in which the jump part is driven by a Poisson random
measure associated to a general L\'evy process and the switching part depends
on the jump diffusion processes. Under broad conditions, the connections of
such stochastic processes and the corresponding partial integro-differential
equations are established. Related initial, terminal, and boundary value
problems are also treated. Moreover, based on weak convergence of probability
measures, it is demonstrated that a sequence of random variables related to the
regime-switching jump diffusion process converges in distribution to the
arcsine law.
