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

Nyberg, Markus ; Ambjörnsson, Tobias LU and Lizana, Ludvig (2016) In New Journal of Physics 18(6).
Abstract

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... (More)

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.

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Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
first-passage time, Gaussian stationary process, independent interval approximation, non-Markovian, particle escape, stochastic processes, symmetric random walk
in
New Journal of Physics
volume
18
issue
6
article number
063019
publisher
IOP Publishing
external identifiers
  • scopus:84976878188
  • wos:000379296000001
ISSN
1367-2630
DOI
10.1088/1367-2630/18/6/063019
language
English
LU publication?
yes
id
9df5d246-e52c-4d74-a74d-2646e9e815fd
date added to LUP
2017-01-25 13:52:49
date last changed
2025-01-12 20:12:32
@article{9df5d246-e52c-4d74-a74d-2646e9e815fd,
  abstract     = {{<p>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.</p>}},
  author       = {{Nyberg, Markus and Ambjörnsson, Tobias and Lizana, Ludvig}},
  issn         = {{1367-2630}},
  keywords     = {{first-passage time; Gaussian stationary process; independent interval approximation; non-Markovian; particle escape; stochastic processes; symmetric random walk}},
  language     = {{eng}},
  month        = {{06}},
  number       = {{6}},
  publisher    = {{IOP Publishing}},
  series       = {{New Journal of Physics}},
  title        = {{A simple method to calculate first-passage time densities with arbitrary initial conditions}},
  url          = {{http://dx.doi.org/10.1088/1367-2630/18/6/063019}},
  doi          = {{10.1088/1367-2630/18/6/063019}},
  volume       = {{18}},
  year         = {{2016}},
}