The Wikipedia article of the Brownian motion states that:
"In the general case, Brownian motion is a non-Markov random process and described by stochastic integral equations."
I find it hard to see why that is the case. I know the Brownian Motion to have independent increments, which seems to be stronger than the markov chain. Also The article for Markov chain has a table that names the Wiener Process as an example of a continuous-time, general state-space MC. Which one is true?
If you look at the reference it gives for this statement, it is
Morozov, A. N.; Skripkin, A. V. (2011). "Spherical particle Brownian motion in viscous medium as non-Markovian random process". Physics Letters A. 375 (46): 4113–4115.
So this is not referring to the Wiener process (what a mathematician would call Brownian motion), but rather to a model of the motion of a physical particle. It is not Markovian, I suppose, because the motion of the sphere causes disturbances of the medium which affect the sphere at later times.