A note on the first-passage problem and VanMarcke's approximation - short communication

被引：8

作者：

Koutsourelakis, P. S. ^{[1
]}

机构：

[1] Lawrence Livermore Natl Lab, Appl Stat & Econ Elect Engn Technol Div, Livermore, CA 94551 USA

来源：

PROBABILISTIC ENGINEERING MECHANICS | 2007年 / 22卷 / 01期

关键词：

first-passage problem; binary process; Markov process;

D O I：

10.1016/j.probengmech.2006.05.003

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

Given a scalar, stationary, Markov process, this short communication presents a closed-form solution for the first-passage problem for a fixed threshold b. The derivation is based on binary processes and the general formula of Siegert [Siegert AJF. On the first-passage time probability problem. Physical Review 195 1; 81:617-23]. The relation for the probability density function of the first-passage time is identical to the commonly used formula that was derived by VanMarcke [VanMarcke E. On the distribution of the first-passage time for normal stationary random processes. Journal of Applied Mechanics ASME 1975; 42:215-20] for Gaussian processes. The present derivation is based on more general conditions and reveals the criteria for the validity of the approximation. Properties of binary processes are also used to derive a hierarchy of upper bounds for any scalar process. (C) 2006 Elsevier Ltd. All rights reserved.

引用

页码：22 / 26

页数：5

共 50 条

[41] A note on first-passage times of continuously time-changed Brownian motion
Hieber, Peter
Scherer, Matthias
STATISTICS & PROBABILITY LETTERS, 2012, 82 (01) : 165 - 172
[42] Mean First-Passage Time and Robustness of Complex Cellular Mobile Communication Network
Liu, Jia-Bao
Zhang, Xue
Cao, Jinde
Chen, Liping
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING, 2024, 11 (03): : 3066 - 3076
[43] First-Passage Problem in Random Vibrations With Radial Basis Function Neural Networks
Wang, Xi
Jiang, Jun
Hong, Ling
Sun, Jian-Qiao
JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, 2022, 144 (05):
[44] HIGHER-ORDER REGULARITY OF THE FREE BOUNDARY IN THE INVERSE FIRST-PASSAGE PROBLEM
Chen, Xinfu
Chadam, John
Saunders, David
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2022, 54 (04) : 4695 - 4720
[45] First-passage problem of strongly nonlinear stochastic oscillators with external and internal resonances
Wu, Y. J.
Gao, Y. Y.
Zhang, L.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, 2013, 39 : 60 - 68
[46] Data-driven identification for approximate analytical solution of first-passage problem
Chen, Xi
Jin, Xiaoling
Huang, Zhilong
PROBABILISTIC ENGINEERING MECHANICS, 2023, 73
[47] EXPECTED FIRST-PASSAGE TIME FOR A SUFFICIENT STATISTIC ARISING IN THE POISSON DISORDER PROBLEM
WICKWIRE, K
JOURNAL OF APPLIED PROBABILITY, 1979, 16 (02) : 274 - 286
[48] Upper Bounds on Liouville First-Passage Percolation and Watabiki's Prediction
Ding, Jian
Goswami, Subhajit
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2019, 72 (11) : 2331 - 2384
[49] First-passage percolation in random planar maps and Tutte's bijection
Lehericy, Thomas
ELECTRONIC JOURNAL OF PROBABILITY, 2022, 27
[50] First-passage time for Sinai's random walk in a random environment
Hong, Wenming
Sun, Mingyang
JOURNAL OF APPLIED PROBABILITY, 2024,

← 1 2 3 4 5 →