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Face of Tobias Ambjörnsson. Photo.

Tobias Ambjörnsson

Senior lecturer

Face of Tobias Ambjörnsson. Photo.

A simple method to calculate first-passage time densities with arbitrary initial conditions

Author

  • Markus Nyberg
  • Tobias Ambjörnsson
  • Ludvig Lizana

Summary, in English

Numerous applications all the way from biology and physics to economics depend on the density of first crossings over a boundary. Motivated by the lack of general purpose analytical tools for computing first-passage time densities (FPTDs) for complex problems, we propose a new simple method based on the independent interval approximation (IIA). We generalise previous formulations of the IIA to include arbitrary initial conditions as well as to deal with discrete time and non-smooth continuous time processes. We derive a closed form expression for the FPTD in z and Laplace-transform space to a boundary in one dimension. Two classes of problems are analysed in detail: discrete time symmetric random walks (Markovian) and continuous time Gaussian stationary processes (Markovian and non-Markovian). Our results are in good agreement with Langevin dynamics simulations.

Department/s

  • Department of Astronomy and Theoretical Physics

Publishing year

2016-06-01

Language

English

Publication/Series

New Journal of Physics

Volume

18

Issue

6

Document type

Journal article

Publisher

IOP Publishing

Topic

  • Computational Mathematics

Keywords

  • first-passage time
  • Gaussian stationary process
  • independent interval approximation
  • non-Markovian
  • particle escape
  • stochastic processes
  • symmetric random walk

Status

Published

ISBN/ISSN/Other

  • ISSN: 1367-2630