Quick search Find article
Quick search
Find article

Asymptotics of rare events in birth–death processes bypassing the exact solutions

Charles R Doering1, Khachik V Sargsyan1, Leonard M Sander2 and Eric Vanden-Eijnden3

Show affiliations


We investigate the near-continuum asymptotics of mean first passage times in some one-variable birth–death processes. The particular problem we address is how to extract mean first passage times in the near-continuum limit from their defining finite-difference equations alone. For the simple class of processes we consider here, exact closed-form solutions for the mean first passage time between any two states are available and the near-continuum expansion of these formulae defines the correct limiting behaviour and is used to check the results of asymptotic analysis of the difference equations. We find that in some cases the asymptotic approach does not lead unequivocally to the proper result.


PACS

87.23.Cc Population dynamics and ecological pattern formation

02.70.Bf Finite-difference methods

Subjects

Computational physics

Environmental and Earth science

Dates

Issue 6 (14 February 2007)

Received 4 September 2006

Published 22 January 2007



  1. Asymptotics of rare events in birth–death processes bypassing the exact solutions

    Charles R Doering et al 2007 J. Phys.: Condens. Matter 19 065145

  2. Applications of field-theoretic renormalization group methods to reaction–diffusion problems

    Uwe C Täuber et al 2005 J. Phys. A: Math. Gen. 38 R79

  3. Generalized supersymetric boundary state

    Koji Hashimoto JHEP04(2000)023

  4. Mean kinetic energy of helium atoms in fluid 3He and 3He–4He mixtures

    C Andreani et al 2006 J. Phys.: Condens. Matter 18 5587

  5. Anomalous kinetic energies of adsorbed 4He on active carbon fibre (ACF)

    D Nemirovsky et al 1999 J. Phys.: Condens. Matter 11 6653

  6. Electromagnetic negative-phase-velocity propagation in the ergosphere of a rotating black hole

    Tom G Mackay et al 2005 New J. Phys. 7 171

  7. Committed ecosystem change due to climate change

    Chris Jones et al 2009 IOP Conf. Ser.: Earth Environ. Sci. 6 062017

Related review articles

What's this?
View review articles related to this research to gain an insight into the key trends in this subject area. Related review articles are selected based on PACS/MSC codes, and are no more than three years old.

  1. 21st century: what is life from the perspective of physics?

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.