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I am trying to do some computations using Laplace transforms in R. I used the
continued fractions approach to compute Laplace transform of a birth-death
process as described in Abate 1999. But I cannot find a simple numerical routine to compute the inverse Laplace transform (evaluated at 0 in my case). Does anyone have ideas on how to do this in R?
Computing inverse Laplace transforms numerically is tricky. I remember seeing some relatively recent results on the ACM. Googling around a bit, I found some
Python code implementing one of these algorithms. Maybe you can adapt it to your purposes.