Proof of Markov propoerty for Ehrenfest urn - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T07:17:21Z http://mathoverflow.net/feeds/question/89536 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/89536/proof-of-markov-propoerty-for-ehrenfest-urn Proof of Markov propoerty for Ehrenfest urn sigma_z_1980 2012-02-26T00:58:56Z 2012-02-26T00:58:56Z <p>In many books Ehrenfest Urn is used as an example of a homogeneous Markov chain, where entries in transition probabilities depend on the state, e.g. </p> <p>$$p_{i,i+1} = \frac{i}{n}, q_{i,i-1} = 1- \frac{i}{n}$$ </p> <p>or, in recurrent notation, for period $t$:</p> <p>$$S_{t} = S_{t-1} + \xi_{t-1}$$ where $\xi_{t-1}$ is a random variable. What I have never seen is the proof that this process satisfies weak Markov property: </p> <p>$$P(S_{t+1} = i_{t+1}|S_{t} = i_{t},...,S_{0}=i_{0}) = P(S_{t+1} = i_{t+1}|S_{t} = i_{t})$$</p> <p>Only in Flajolet, Dumas,Puyhaubert(2006) on p.70 it is mentioned that Ehrenfest urn can be viewed as a random walk on N-dimensional cube, but I can't relate it.</p> <p>I'd massively appreciate suggestion on how to approach this proof. </p>