Strictness of Markov Properties

A stochastic process {Xi}i=0 is n-Markov if P(Xt+n|Xt+n1,Xt+n2,,Xt)=P(Xt+n|Xt+n1)for any t0. We would prove that An n-Markov stochastic process must be m-Markov while is not necessarily l-Markov where l>n>m N+1 to N First, we prove an (n+1)-Markov stochastic process must be n-Markov. Proof: Suppose {Xi}i=0 is an (n+1)-Markov stochastic process. We have P(Xt+n|Xt+n1,Xt+n2,,Xt)=P(Xt+n|Xt+n1) for any t0, deriving ...

August 28, 2023 · 2 min