DIXIE - math.ubc.ca
6
Timereversibility Let Xlt be an irreducible CTMC with stationary distribution T Assume that X o NT so that for all 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 in state 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.ir PCXCts i PfXlt s ir3 Xt sr i PXt r i aXlt Pat i 7 Vir Fi Exp Vi t r e true that I spends in state i
Transcript of DIXIE - math.ubc.ca
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