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math.PR2013
Reinforced Brownian Motion on the Half-Line
Jerome K. Percus, Ora E. Percus
We analyze the Brownian Motion limit of a prototypical unit step reinforced random-walk on the half line. A reinforced random walk is one which changes the weight of any edge (or v…
math.PR2013
The maximum of a symmetric next neighbor walk on the non-negative integers
Jerome K. Percus, Ora E. Percus
We consider a one-dimensional discrete symmetric random walk with a reflecting boundary at the origin. Generating functions are found for the 2- dimensional probability distributio…