Monotonicity of Recurrence in Random Walks
arxiv(2024)
摘要
We consider non-homogeneous random walks on the positive quadrant in two
dimensions. In the 1960's the following question was asked: is it true if such
a random walk X is recurrent and Y is another random walk that at every
point is more likely to go down and more likely to go left than Y, then Y
is also recurrent?
We provide an example showing that the answer is negative. We also show that
if either the random walk X or Y is sufficiently homogeneous then the
answer is in fact positive.
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