In the current literature we can find mainly two approaches to the
SDE regime switching modeling. The traditional one, the externally induced
regime switching diffusions is described by the switching being derived from
a separate continuous time Markov process, with a finite, or denumerable,
state space { indexing the regimes { the random times of the regime switches
being exactly the jump times of the finite valued Markov process. There is a
first alternative approach in which the regime switching occurs whenever the
trajectory enters in some prescribed region on the state space; the regions we
consider will be mainly open intervals defined by unknown thresholds for the
trajectories; thresholds that, in principle, should also be estimated. In this
approach the partitioning of the the state space is already defined in the drift
and volatility of the SDE. In a second alternative approach the switching occurs
in a random way but at some random times defined when the trajectories hit
some prescribed thresholds, that again, must be estimated. We may designate
these two alternative approaches as auto-induced regime switching diffusions
as there is no external noise source to force the switching occurrence. We prove
a generalization of an existence result of the existence of auto-induced regime
switching SDE solutions for irregular coefficients and a result that encompasses
some of the cases of both externally and auto-induced regime switching SDE
solutions.