科研之友
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摘要
We study a one-dimensional Brownian motion conditioned on a self-repelling behaviour. Given a nondecreasing positive function f(t), t >= 0, consider the measures mu(t) obtained by conditioning a Brownian. path so that L(s) <= f(s), for all s <= t, where L(s) is the local time spent at the origin by time s. It is shown that the measures mu(t) are tight, and that any weak limit of mu(t) as t -> infinity is transient provided that t(-3/2) f(t) is integrable. We conjecture that this condition is sharp and present a number of open problems.
- 出版日期2011-5
