Estimation of the Moments of the Residence Time and First Passage Time from Experimentally Measurable Permeation Parameters via a New Formulation of the Transmission Matrix

2014 ◽  
Vol 61 (8) ◽  
pp. 867-874 ◽  
Author(s):  
Jenn-Shing Chen ◽  
Kwei-Tin Yeh ◽  
Wen-Yih Chang ◽  
James K. Baird
Keyword(s):  
Residence Time ◽  
First Passage Time ◽  
Passage Time ◽  
Transmission Matrix ◽  
First Passage ◽  
New Formulation

scholarly journals APLIKASI MODEL RANTAI MARKOV UNTUK MENGANALISIS TINGKAT KENYAMANAN DI KOTA MAJENE BERDASARKAN TEMPERATURE HUMIDITY INDEX (THI)

2021 ◽  
Vol 15 (1) ◽  
pp. 009-014
Author(s):  
Muhammad Abdy ◽  
Wahidah Sanusi ◽  
Rahmawati Rahmawati
Keyword(s):  
Steady State ◽  
Residence Time ◽  
Mean Residence Time ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Temperature Humidity Index ◽  
Humidity Index ◽  
The Mean

This study applied the Markov chain model on the daily temperature and relative humidity data that was collected from the Meteorology and Geophysics Agency station in Majene district for the period 1983 to 2011. This study aims to analyze the comfortable level category in the Majene city based on the Temperature Humidity Index by calculating the probability of steady-state, the mean residence time and the mean first passage time. Categorizing the level of comfortable which is based on the Temperature Humidity Index consists of three categories, namely the comfortable, quite comfortable and uncomfortable. The trend of comfortable levels in the Majene city from 1983 to 2011 was fluctuated in the categories of quite comfortable and uncomfortable. Uncomfortable category occurs in October and November each year. The steady-state probability values indicates that the quite comfortable category has the highest chance of appearance, which is around 70%, and the comfortable category has the smallest chance of appearance, which is only about 5%. Meanwhile, the mean residence time and the mean first passage time indicate that the quite comfortable category have the longest duration of occurrence, which is around 5 days, and has the shortest duration to recur after occurring in the previous event, which is around 1.43 days.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap

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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