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原文連結
論文資訊
- 類型：已發表論文
- 日期：2015-06-30
摘要
We investigate some simple and surprising properties of a one-dimensional Brownian trajectory with 擴散 coefficient D that starts at the origin and: (i) is at X at time T, or (ii) first reaches X at time T. We determine the most likely location of the first-passage trajectory from (0, 0) to ( X, T) and its distribution at any intermediate time t < T. A first-passage path typically starts out by being repelled from its final location when X-2/DT << 1. We also determine the distribution of times when the trajectory first crosses and last crosses an arbitrary intermediate position x < X. The distribution of first-crossing times may be unimodal or bimodal, depending on whether X-2/DT << 1 or X-2/DT << 1. The form of the first-crossing probability in the bimodal regime is qualitatively similar to
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