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The inverse first-passage-place problem for Wiener processes
Stochastic Analysis and Applications ( IF 1.3 ) Pub Date : 2021-02-23 , DOI: 10.1080/07362994.2021.1889382 Mario Lefebvre 1
中文翻译:
维纳过程的逆首通道问题
更新日期:2021-02-23
Stochastic Analysis and Applications ( IF 1.3 ) Pub Date : 2021-02-23 , DOI: 10.1080/07362994.2021.1889382 Mario Lefebvre 1
Affiliation
Abstract
Let be a Wiener process with infinitesimal mean μ and variance 1, starting at . Assume that X(0) is a random variable and define τ to be the first time that X(t) = 0 or 1. We look for probability density functions of X(0) such that . Various cases are considered both when μ = 0 and
中文翻译:
维纳过程的逆首通道问题
摘要
让 是一个具有无穷小均值μ和方差 1的维纳过程,从. 假设X (0) 是一个随机变量,并将τ定义为X ( t ) = 0 或 1的第一次。我们寻找X (0) 的概率密度函数,使得. 当μ = 0 和