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A Non-Markovian Version of Pitman's 2M - X Theorem

Hambly, Ben M.; Martin, James; O'Connell, Neil


Keyword(s): Pitman's representation theorem; telegrapher's process

Abstract: Please Note. This abstract contains mathematical formulae which cannot be represented here. Let ( k, k 0) be a Markov chain on {-1, +1} with 0 = 1 and transition probabilities P ( k+1 = 1 k =1) = a and P ( k+1 = - 1 k = -1) = ba>b>0. Set X0 =0, Xn = 1 +???+ n and Mn = max0 k n Xk. Notes: Ben Hambly, St Annes College, University of Oxford, Oxford, UK James Martin, Statistical Laboratory, Cambridge University, Cambridge, UK

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