A two-parameter random walk with approximate exponential probability distribution
arXiv:math-ph/0512077 · doi:10.1088/0305-4470/39/23/005
Abstract
We study a non-Markovian random walk in dimension 1. It depends on two parameters eps_r and eps_l, the probabilities to go straight on when walking to the right, respectively to the left. The position x of the walk after n steps and the number of reversals of direction k are used to estimate eps_r and eps_l. We calculate the joint probability distribution p_n(x,k) in closed form and show that, approximately, it belongs to the exponential family.
12 pages, updated reference to companion paper cond-mat/0601263