Numerical Computation of First-Passage Times of Increasing Lévy Processes

By Mark S. Veillette, Murad S. Taqqu. 2009

47 citations recorded by the source corpus.

Let {D(s), s ≥ 0} be a non-decreasing Lévy process. The first-hitting time process {E(t), t ≥ 0} (which is sometimes referred to as an inverse subordinator) defined by $E(t) = \inf \{s: D(s) > t \}$ is a process which has arisen in many applications. Of particular interest is the mean first-hitting time $U(t)=\mathbb{E}E(t)$. This function characterizes all finite-dimensional distributions of the process E. The function U can be calculated by inverting the Laplace transform of the function $\widetilde{U}(\lambda) = (\lambda \phi(\lambda))^{-1}$, where ϕ is the Lévy exponent of the subordinator D. In this paper, we give two methods for computing numerically the inverse of this Laplace transform. The first is based on the Bromwich integral and the second is based on the Post-Widder inversion formula. The software written to support this work is available from the authors and we illustrate its use at the end of the paper.

Subfields: Applied Mathematics, Modeling and Simulation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5d89f4fc78a61986764d86c34d32355873c55e51

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In Applied Mathematics

  1. Andreas E. Kyprianou
  2. Arun Kumar
  3. V. Rivero
  4. Alexey Kuznetsov
  5. Palaniappan Vellaisamy
  6. Lotfi Boudabsa
  7. Pierre Patie
  8. Mladen Savov

In Modeling and Simulation

  1. Arun Kumar
  2. V. Rivero
  3. Alexey Kuznetsov
  4. Andreas E. Kyprianou
  5. Palaniappan Vellaisamy

In Statistics and Probability

  1. Andreas E. Kyprianou
  2. V. Rivero
  3. Alexey Kuznetsov
  4. Arun Kumar
  5. Palaniappan Vellaisamy
  6. Zhan Shi
  7. Xiaowen Zhou
  8. Nathalie Krell

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