Markov Prediction

A type of Markov Inference for predicting future state distributions without new evidence. $P(X_{t+k}\mid e_{1:t})$ Prediction is Filtering without new evidence, so the proof for the next formula is the same.

$\mathrm{P}\left({\mathrm{X}}_{t+k+1}\mid {\mathrm{e}}_{1:t}\right)={\sum }_{{\mathrm{x}}_{t+k}}\mathrm{P}\left({\mathrm{X}}_{t+k+1}\mid {\mathrm{x}}_{t+k}\right)\cdot P\left({\mathrm{x}}_{t+k}\mid {\mathrm{e}}_{1:t}\right)$