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A two-parameter random walk with approximate exponential probability distribution

Erik Van der Straeten·Jan Naudts
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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.

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Erik Van der Straeten, Jan Naudts. 2006-01-17. A two-parameter random walk with approximate exponential probability distribution. https://doi.org/10.1088/0305-4470%2F39%2F23%2F005

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