scholarly journals The Passage Time Distribution for a Birth-and-Death Chain: Strong Stationary Duality Gives a First Stochastic Proof

2009 ◽  
Vol 22 (3) ◽  
pp. 543-557 ◽  
Author(s):  
James Allen Fill
Keyword(s):  
Time Distribution ◽  
Passage Time ◽  
Strong Stationary Duality ◽  
Birth And Death Chain

Identifying Coefficients in the Spectral Representation for First Passage Time Distributions

1987 ◽  
Vol 1 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Mark Brown ◽  
Yi-Shi Shao
Keyword(s):  
Markov Processes ◽  
Time Distribution ◽  
Infinitesimal Generator ◽  
Spectral Representation ◽  
First Passage Time ◽  
Passage Time ◽  
Spectral Approach ◽  
Generator Matrix ◽  
Eigenvalues And Eigenvectors ◽  
First Passage

The spectral approach to first passage time distributions for Markov processes requires knowledge of the eigenvalues and eigenvectors of the infinitesimal generator matrix. We demonstrate that in many cases knowledge of the eigenvalues alone is sufficient to compute the first passage time distribution.

Burke's theorem on passage times in Gordon–Newell networks

1984 ◽  
Vol 16 (04) ◽  
pp. 867-886
Author(s):  
Hans Daduna
Keyword(s):  
Cycle Time ◽  
Time Distribution ◽  
Passage Time ◽  
The Other ◽  
Single Server ◽  
Closed Cycle ◽  
Closed Networks ◽  
Multiserver Queues ◽  
Simple Product ◽  
Passage Times

In a closed cycle of exponential queues where the first and the last nodes are multiserver queues while the other nodes are single-server queues, the cycle-time distribution has a simple product form. The same result holds for passage-time distributions on overtake-free paths in Gordon–Newell networks. In brief, we prove Burke's theorem on passage times in closed networks.

Burke's theorem on passage times in Gordon–Newell networks

1984 ◽  
Vol 16 (4) ◽  
pp. 867-886 ◽  
Author(s):  
Hans Daduna
Keyword(s):  
Cycle Time ◽  
Time Distribution ◽  
Passage Time ◽  
The Other ◽  
Single Server ◽  
Closed Cycle ◽  
Closed Networks ◽  
Multiserver Queues ◽  
Simple Product ◽  
Passage Times

In a closed cycle of exponential queues where the first and the last nodes are multiserver queues while the other nodes are single-server queues, the cycle-time distribution has a simple product form. The same result holds for passage-time distributions on overtake-free paths in Gordon–Newell networks. In brief, we prove Burke's theorem on passage times in closed networks.

scholarly journals On the First Passage Time Distribution for a Class of Markov Chains

1983 ◽  
Vol 11 (4) ◽  
pp. 1000-1008 ◽  
Author(s):  
Mark Brown ◽  
Narasinga R. Chaganty
Keyword(s):  
Markov Chains ◽  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage

Evaluation of the first-passage time probability to a square root boundary for the Wiener process

1977 ◽  
Vol 14 (4) ◽  
pp. 850-856 ◽  
Author(s):  
Shunsuke Sato
Keyword(s):  
Wiener Process ◽  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
Square Root ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Asymptotic Evaluation

This paper gives an asymptotic evaluation of the probability that the Wiener path first crosses a square root boundary. The result is applied to estimate the moments of the first-passage time distribution of the Ornstein–Uhlenbeck process to a constant boundary.

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