Recurrence times of clusters of Poisson points

1969 ◽  
Vol 6 (02) ◽  
pp. 372-388 ◽  
Author(s):  
R.T. Leslie
Keyword(s):  
Laplace Transform ◽  
Continuous Time ◽  
Distribution Functions ◽  
Numerical Inversion ◽  
Bernoulli Trials ◽  
Recurrence Times ◽  
Failure Patterns ◽  
The Laplace Transform

In a previous paper (Leslie (1967)) the distribution of recurrence times for a particular set of success-failure patterns on a sequence of Bernoulli trials was investigated. We now consider the analogous events in continuous time and obtain the Laplace Transform (L.T.) of the distribution of recurrence times; numerical inversion yields the distribution functions.

Recurrence times of clusters of Poisson points

1969 ◽  
Vol 6 (2) ◽  
pp. 372-388 ◽  
Author(s):  
R.T. Leslie
Keyword(s):  
Laplace Transform ◽  
Continuous Time ◽  
Distribution Functions ◽  
Numerical Inversion ◽  
Bernoulli Trials ◽  
Recurrence Times ◽  
Failure Patterns ◽  
The Laplace Transform

In a previous paper (Leslie (1967)) the distribution of recurrence times for a particular set of success-failure patterns on a sequence of Bernoulli trials was investigated. We now consider the analogous events in continuous time and obtain the Laplace Transform (L.T.) of the distribution of recurrence times; numerical inversion yields the distribution functions.

scholarly journals Numerical inversion of the Laplace transform

1999 ◽  
Vol 110 (23) ◽  
pp. 11176-11186 ◽  
Author(s):  
Bruno Hüpper ◽  
Eli Pollak
Keyword(s):  
Laplace Transform ◽  
Numerical Inversion ◽  
The Laplace Transform

scholarly journals The noise handling properties of the Talbot algorithm for numerically inverting the Laplace transform

2018 ◽  
Vol 13 ◽  
pp. 174830181879706 ◽  
Author(s):  
Colin L Defreitas ◽  
Steve J Kane
Keyword(s):  
Fourier Series ◽  
Laplace Transform ◽  
Noisy Data ◽  
Standard Test ◽  
Numerical Inversion ◽  
Test Functions ◽  
Inversion Algorithm ◽  
Inverse Transform ◽  
Exact Data ◽  
The Laplace Transform

This paper examines the noise handling properties of three of the most widely used algorithms for numerically inverting the Laplace transform. After examining the genesis of the algorithms, their error handling properties are evaluated through a series of standard test functions in which noise is added to the inverse transform. Comparisons are then made with the exact data. Our main finding is that the for “noisy data”, the Talbot inversion algorithm performs with greater accuracy when compared to the Fourier series and Stehfest numerical inversion schemes as they are outlined in this paper.

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