当平均值不够时：计算出生-死亡过程中的注视时间分布
When the mean is not enough: Calculating fixation time distributions in birth-death processes
摘要：
马尔可夫过程中的固定动力学研究主要集中在平均吸收时间。如果分布广泛且不均衡，这可能是不够的。计算了具有两个吸收态的一步生灭过程中注视时间的分布。这些都表示在频谱的过程中，我们提供了不同的表示为前向只在本征空间的过程。这些允许有效采样的固定时间分布。作为一个应用程序，我们研究进化博弈动力学，入侵突变体可以达到固定或灭绝。我们还强调了中位数固定时间作为一个可能的模拟混合时间的系统中的突变率小，没有吸收状态，而平均固定时间没有这样的解释。
英文摘要：
Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death processes with two absorbing states. These are expressed in terms of the spectrum of the process, and we provide different representations as forward-only processes in eigenspace. These allow efficient sampling of fixation time distributions. As an application we study evolutionary game dynamics, where invading mutants can reach fixation or go extinct. We also highlight the median fixation time as a possible analog of mixing times in systems with small mutation rates and no absorbing states, whereas the mean fixation time has no such interpretation.
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