TimereversibilityLet Xlt be an irreducible CTMC with stationary

distribution T Assume that X o NT so that forall t O X ft rt as well

Thereversedprocess s Fix a large t and consider

the reverse chain s X t s for Osset

Claim conditional on I10 _i the lime IT spends instate i is Exp Vi just like X

Proof PCF zr

P X s i for se o r I 10 i

P X t s i for se 0 DIXIE i

PCXCt sl iforseco.irPCXCts i

PfXlt s ir3 Xt sr i PXt r i

aXltPat i

7 Vir Fi Exp Vit r etrue that I spends in state i