Talk:Markov property

message: The old article called Markov property didn't even correctly define the property, confusing it with the process. That was a mess. So I created a new article.  linas (talk) 22:29, 30 August 2008 (UTC)
thread_title: Brand new article

message: Does someone have a reference that does use the term "Markov property" in the sense suposedly used here? The reference to Feller doesn't do so I think ... The chapter/section mentioned seems to be about Markov processes and, while "Markov property" is in the index that points to a definition on other pages in connection with the "memoryless" property of the exponential distribution.
If the definition here is relevant to anything, what is the role of the index j? For a "Markov property" to hold does the stated condition have to hold for every j, or for only one j? Presumably Nj must exclude at least one other member besides j, but is it enough for this to apply for only one j?
Melcombe (talk) 17:58, 22 January 2009 (UTC)
thread_title:  Doubts 

message: You know what I just LOVE?
I really love it when an article about math, computer science, statistics, etc. has a whole bunch of terms that are never defined.
This article needs someone to come in and describe for us what the various variables and symbols in the text are referring to.
It would be really nice to have the ℝdefined, and maybe the Ω, or β (that is a beta, and not a 'B' isn't it... See, that is what I am talking about*), or the funny shaped 'F'. Heck, it would have been nice to know what the 't' means, even though this traditionally means 'Time" in math. I'm pretty sure that the P is a "Probability" (ℙ). Dang, even the X isn't defined here.
In fact, the whole series of articles on Markov's work needs to have this done. Some at least let you know what some of the variables are defined as, but most just have these arcane strings of letters and symbols that leave anyone who doesn't have a DEEP math background scratching their heads, completely unable to make ANY sense of the article without spending an hour of so searching (possibly in futility) for what these terms mean.
* and regardless of whether it is a 'B' or a 'Beta' it needs to be defined. Not everyone who comes to this page will be some math geek or computer nerd who knows what these terms mean or if they are referring to real world objects or other conceptual objects/subjects. I mean, please give us a SLIGHT clue as to what a Borel sigma-algebra is... just a hint, you don't have to cite the whole page, but not having to go link-diving really helps.
Matthew R Bailey (talk) 15:16, 18 November 2011 (UTC)
thread_title:  November 2011 - Definitions of terms 

message: The statement of the strong Markov property is wrong (in the case tau:=t it reduces to X_{t+} is independent of F_t what is definitely wrong!). The essential statement is that X_{tau+} is independent of F_{tau} given X_{tau}. In this formulation the statement is only reasonable for time-homogeneous processes (as mentioned). However the statement X_{tau+} independent of F_{tau} given the pair (tau,X_{tau}) makes sense for any Markov process. Moreover there is a small mistake in the definition of F_{tau}. The intersection of tau and A does not make sense - it should be the intersection of A with the event {tau=t}.  — Preceding unsigned comment added by 141.5.26.78 (talk) 11:38, 5 April 2013 (UTC)
thread_title: Mistake in definition of strong Markov property

message: I don't like the notion of time the description of the Markov property gives here.
The Markov property is here explained in terms of future and past. This can be very confusing since it can give a notion of an absolute time which is not the case. A Markov process is characterised by it’s behaviour in relation to it’s preceding states, so relative to some state which can be in the past or not. In many cases the states of a process are not even functions of time, as for instance in the case of a DNA sequence or text.
I think it makes more sense to define it as a dependence on only it's single preceding state. This is the way Vaseghi goes in this book "Advanced Digital Signal Processing" and I find that much better since it removes the unnecessary confusion about time.  — Preceding unsigned comment added by Mijamaka (talk • contribs) 15:44, 10 April 2017 (UTC)
thread_title:  Misleading notion of time 

message: It might be good idea to precise where the formula in the "Alternative formulation" section comes from.
The reference given states a formulation using conditional expectations but it seems interpreted in a weird way. (In the book, there is both indexes t and t+h that appear in the formulation) 194.214.86.1 (talk) 13:46, 11 October 2023 (UTC)
thread_title:  Alternative formulation