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

$\displaystyle Q_{t+1}=MQ_t$

which gives the recurrence relation

$\displaystyle Q_t = M^tQ_0$

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

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

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