Markov additive process
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A Markov additive process (MAP) is a bivariate Markov process whose transition probability measure is translation invariant in the additive component . Çinlar uses the unique structure of
the MAP to prove that, given a gamma process with a shape parameter
that is a function of Brownian motion, the resulting lifetime is
distributed according to the Weibull distribution.
Kharoufeh presents a compact transform expression
for the failure distribution for wear processes of a component
degrading according to a Markovian environment inducing
state-dependent continuous linear wear by using the properties of a
MAP and assuming the wear process to be temporally homogeneous and
that the environmental process has a finite state space.
