Line crossing problem for biased monotonic random walks in the plane
نویسنده
چکیده
In this paper, we study the problem of finding the probability that the two-dimensional (biased) monotonic random walk crosses the line y = αx+d, where α, d ≥ 0. A β-biased monotonic random walk moves from (a, b) to (a + 1, b) or (a, b + 1) with probabilities 1/(β + 1) and β/(β + 1), respectively. Among our results, we show that if β ≥ ⌈α⌉, then the β-biased monotonic random walk, starting from the origin, crosses the line y = αx+ d for all d ≥ 0 with probability 1.
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