I have been reading the Probability Theory notes by Prof. Amir Dembo (available here) and I came across this property of Markov Processes which says that Markov Processes are invariant under 'invertible monotone time mappings' and I am not too sure that I understand this.
According to me this property means that time homogeneous Markov Processes are invariant under invertible and continuous functions. However, I am not sure at all if my understanding is correct. Just incase, it is indeed correct, then I fail to understand why is it that the Markov Processes possess this property.
Does it further imply that this property holds true also for time homogeneous diffusion processes?
Any help is much appreciated!