Representations of the first hitting time density of an Ornstein-Uhlenbeck process
Representations of the first hitting time density of an Ornstein-Uhlenbeck process
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DOI：
10.1080/15326340500294702
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发表时间：
2005-01-01
影响因子：
0.7
通讯作者：
Pedersen, JL
中科院分区：
文献类型：
--
作者：
Alili, A;Patie, P;Pedersen, JL
给出了Ornstein-Uhlenbeck过程达到某一固定水平的首击时间密度的三个表达式。第一个问题依赖于涉及抛物柱面函数零点的本征值展开。第二个是涉及一些特殊函数的积分表示，而第三个是根据三维贝塞尔徽章的泛函给出的。这些表达式用于近似密度。
Three expressions are provided for the first hitting tine density of an Ornstein-Uhlenbeck process to reach a fixed level. The first hinges on an eigenvalue expansion involving zeros of the parabolic cylinder functions. The second is an, integral representation involving some special functions whereas the third is given in terms of a functional of a 3-dimensional Bessel badge. The expressions are used for approximating the density.