Laplace Transform Inversion and Passage-Time Distributions in Markov Processes

  title={Laplace Transform Inversion and Passage-Time Distributions in Markov Processes},
  author={Peter G. Harrison},
  journal={Journal of Applied Probability},
  • P. Harrison
  • Published 1 March 1990
  • Mathematics
  • Journal of Applied Probability
Products of the Laplace transforms of exponential distributions with different parameters are inverted to give a mixture of Erlang densities, i.e. an expression for the convolution of exponentials. The recurrence for the inversion of certain weighted sums of these transforms is then solved by converting it into a linear first-order partial differential equation. The result may be used to find the density function of passage times between states in a Markov process and it is applied to derive an… 
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