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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
Affiliation  

Abstract

Let {X(t),t0} be a Wiener process with infinitesimal mean μ and variance 1, starting at X(0)[0,1]. 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 P[X(τ)=0]=q(0,1). Various cases are considered both when μ = 0 and μ0.



中文翻译:

维纳过程的逆首通道问题

摘要

{X(),0}是一个具有无穷小均值μ和方差 1的维纳过程,从X(0)[0,1]. 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[X(τ)=0]=q(0,1). 当μ  = 0 和μ0.

更新日期:2021-02-23
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