« first day (1 day earlier)  last day (15 days later) » 

15:50
Stupid question, if your transformation is derived by a markov chain I guess it has special properties right? I guess you either have a transition matrix or a transition kernel which very specific properties that might actually make the proof simple.
 
2 hours later…
17:50
I might be onto something, if it is of any interest please get in touch

« first day (1 day earlier)  last day (15 days later) »