Consider an initial vector of state probabilities $$\{P(1)=0, P(2)=p2, P(3)=1-p2, P(4)=0\}$$ At each time period t, a state transition is applied to the vector according to one of the two markov processes below, where $1>\alpha>\frac{1}{2}$: Is there a tractable way to maximize Prob(state=4) aft...

Consider a given state variable $s_0\in\{1,2,3,4\}$ initially distributed according to probabilities $$P(s_0=1)=0, P(s_0=2)=p_2, P(s_0=3)=1-p_2, P(s_0=4)=0.$$ At each time period $t\in 1..T$, a state transition is applied to the vector of probabilities according to one of the two markov processes...