User talk:Obsolete.fax

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Talk:Stochastic_matrix

[edit] Stochastic matrix

I'll take a look at it sometime in the next few weeks. It's quite a lot to absorb, and I'm going out of town shortly. sorry to procrastinate. --W0lfie (talk) 21:08, 7 February 2008 (UTC)


It made sense finally when I drew it out, so I'm sharing my cheesy drawing. Appomile (talk) 14:03, 13 February 2008 (UTC) Image:StochasticMatrix--CatMouseGame.PNG

You got it! I'm going to undo your edit to the talk page, though. It's generally considered good form to leave the discussion up so other people with your same questions can see it. Cheers! --W0lfie (talk) 17:43, 12 February 2008 (UTC)

I didn't post my username when I put that pic in. But it was me. Probably not good form there, sorry. Appomile (talk) 14:03, 13 February 2008 (UTC)

oops. I assumed it was Obsolete.fax who did. I should pay closer attention. Either way, maybe it will prove useful. --W0lfie (talk) 21:24, 13 February 2008 (UTC)

[edit] Stochastic matrix Question 4

\mathbf{p}_k = \mathbf{v}P^k \, .
We want to find the probability that the system is in a given state after a given number of time steps. The set of probabilities for each state after k time steps is given by the probability vector pk. The purpose of the formula is that it gives an expression for the probability vector after k time steps in terms of the initial state vector v and the stochastic matric P - so if we know v and P we can find the probability vector at any subsequent time. The "mathematical induction" part just means that we can derive the general formula for pk by looking at the formulae for p1, p2 etc. and then generalising the pattern that we see to k time steps. Can you see where the formulae that I give above for p1, p2 come from ? Can you see how they lead to a general formula for pk ? Gandalf61 (talk) 09:35, 12 February 2008 (UTC)

I am assuming the formulae \mathbf{p}_k = \mathbf{v}P^k \, that you gave above for p1, p2 came from Summation? If this is true then can the formula be put in Sigma notation format \sum_{i=m}^n x_i = x_m + x_{m+1} + x_{m+2} +\cdots+ x_{n-1} + x_n.  ? --Obsolete.fax (talk) 05:28, 17 February 2008 (UTC)