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

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A simple method to calculate first-passage time densities with arbitrary initial conditions. / Nyberg, Markus; Ambjörnsson, Tobias; Lizana, Ludvig.

I: New Journal of Physics, Vol. 18, Nr. 6, 063019, 01.06.2016.

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

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TY - JOUR

T1 - A simple method to calculate first-passage time densities with arbitrary initial conditions

AU - Nyberg, Markus

AU - Ambjörnsson, Tobias

AU - Lizana, Ludvig

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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.

AB - 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.

KW - first-passage time

KW - Gaussian stationary process

KW - independent interval approximation

KW - non-Markovian

KW - particle escape

KW - stochastic processes

KW - symmetric random walk

UR - http://www.scopus.com/inward/record.url?scp=84976878188&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/18/6/063019

DO - 10.1088/1367-2630/18/6/063019

M3 - Article

VL - 18

JO - New Journal of Physics

T2 - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 6

M1 - 063019

ER -