First passage times of stationary non-Gaussian structural responses

2007 ◽  
Vol 85 (7-8) ◽  
pp. 431-436 ◽  
Author(s):  
Jun He ◽  
Yan-Gang Zhao
Keyword(s):  
First Passage Times ◽  
First Passage ◽  
Structural Responses ◽  
Non Gaussian ◽  
Passage Times

Extreme Response of Nonlinear Structures With Low Damping Subjected to Stochastic Loading

1999 ◽  
Vol 121 (4) ◽  
pp. 255-260 ◽  
Author(s):  
A. Naess
Keyword(s):  
Extreme Values ◽  
Narrow Band ◽  
First Passage Times ◽  
Random Loading ◽  
First Passage ◽  
Stochastic Loading ◽  
Extreme Response ◽  
Non Gaussian ◽  
Extreme Responses ◽  
Passage Times

The response of structures with low damping to random loading is generally characterized by significant clumping of the large response peaks. This clumping is known to affect the extreme responses of the structure. In the paper, we shall propose an approximate method to account for this effect on first passage times and extreme values of narrow-band random vibrations, both Gaussian and non-Gaussian. The method is based on the concept of joint crossing rates of a stochastic process. This makes it possible to introduce a correlation structure to the sequence of peak values, allowing the introduction of an approximate estimate of the effect of clumping on large excursions of the underlying narrow-band process. The advantage of the proposed method is that explicit, closed-form expressions for the clumping effect on first passage times and extreme values are obtained. The method is illustrated by application to specific examples.

Inequalities for Means of Restricted First-Passage Times in Percolation Theory

1999 ◽  
Vol 8 (4) ◽  
pp. 307-315 ◽  
Author(s):  
SVEN ERICK ALM ◽  
JOHN C. WIERMAN
Keyword(s):  
Half Space ◽  
Percolation Theory ◽  
First Passage Times ◽  
First Passage ◽  
Geometric Argument ◽  
Convexity And Concavity ◽  
Passage Times

A simple geometric argument establishes an inequality between the sums of two pairs of first-passage times. This result is used to prove monotonicity, convexity and concavity results for first-passage times with cylinder and half-space restrictions.

Spectral Theory for Skip-Free Markov Chains

1989 ◽  
Vol 3 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Joseph Abate ◽  
Ward Whitt
Keyword(s):  
Markov Chains ◽  
Spectral Theory ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage Times ◽  
Simple Relationship ◽  
First Passage ◽  
Birth And Death Processes ◽  
The Laplace Transform ◽  
Passage Times

The distribution of upward first passage times in skip-free Markov chains can be expressed solely in terms of the eigenvalues in the spectral representation, without performing a separate calculation to determine the eigenvectors. We provide insight into this result and skip-free Markov chains more generally by showing that part of the spectral theory developed for birth-and-death processes extends to skip-free chains. We show that the eigenvalues and eigenvectors of skip-free chains can be characterized in terms of recursively defined polynomials. Moreover, the Laplace transform of the upward first passage time from 0 to n is the reciprocal of the nth polynomial. This simple relationship holds because the Laplace transforms of the first passage times satisfy the same recursion as the polynomials except for a normalization.

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