scholarly journals Modeling of semi-competing risks by means of first passage times of a stochastic process

2017 ◽  
Vol 24 (1) ◽  
pp. 153-175 ◽  
Author(s):  
Beate Sildnes ◽  
Bo Henry Lindqvist
Keyword(s):  
Stochastic Process ◽  
Competing Risks ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

Random walk type models for indicator-dilution studies: comparison of a local density random walk and a first passage times distribution

1986 ◽  
Vol 20 (11) ◽  
pp. 789-796 ◽  
Author(s):  
J M BOGAARD ◽  
J R C JANSEN ◽  
E A VON RETH ◽  
A VERSPRILLE ◽  
M E WISE
Keyword(s):  
Random Walk ◽  
Local Density ◽  
Indicator Dilution ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

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.

On the Test and Power of Zero Drift on First Passage Times in Brownian Motion

Technometrics ◽  
1976 ◽  
Vol 18 (3) ◽  
pp. 341-342 ◽  
Author(s):  
S. A. Patil ◽  
J. L. Kovner
Keyword(s):  
Brownian Motion ◽  
First Passage Times ◽  
Zero Drift ◽  
First Passage ◽  
Passage Times

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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