Hello all, I'm hoping that someone out there will be able to provide some insight on this...

When projecting a matrix through time, it seems to be pretty common to use the expression

Q_{t+1}=MQ_t

which gives the recurrence relation

Q_t = M^tQ_0

But what if instead we want to combine the transition with the previous state, and then re-scale the system

Q_{t+1}=((MQ_t+Q_t)/SUM(MQ_t+Q_t))*K (Sum is the row sum)

Is it possible to get a recurrence relation? If so what would it be? Any thoughts?

Thanks,