Out of a pretty big slide deck, explicitly intended for a beginner audience, this is a weird thing to pick on. The following is "Proposition 1.1" from the rele

Out of a pretty big slide deck, explicitly intended for a beginner audience, this is a weird thing to pick on. The following is "Proposition 1.1" from the relevant section of a standard text (Bhattacharya and Waymire): "A stochastic process X0, X1, X2, ... has the Markov property if and only if for each n the conditional distribution of Xn+1 given X0...Xn is a function only of Xn." The only difference between the above Prop. 1.1 and the statement in TFA is that TFA omits to specify it means a conditional distribution of Xt+1 given X1...Xt (as opposed to an unconditional distribution). But, in literally the following line, TFA goes on to clarify what it means by stating the equation that the words correspond to, and the equation has the correct conditional distribution. I don't see reason for alarm here.