Geodesic
On the Expected Number of Visits of a Particle before Absorption in a Correlated Random Walk
Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 389-395

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Let a particle move along a straight line a unit distance during every interval of time τ. During the first interval τ it moves to the right with probability ρ 1 and to the left with probability ρ 2 = 1 - ρ 1. Thereafter at the end of each interval τ, the particle with probability p continues its motion in the same direction as in the previous step and with probability q = l - p reverses it. 
Jain, G. C. On the Expected Number of Visits of a Particle before Absorption in a Correlated Random Walk. Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 389-395. doi: 10.4153/CMB-1973-061-3
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     title = {On the {Expected} {Number} of {Visits} of a {Particle} before {Absorption} in a {Correlated} {Random} {Walk}},
     journal = {Canadian mathematical bulletin},
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     year = {1973},
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     doi = {10.4153/CMB-1973-061-3},
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