Charles R Doering et al 2007 J. Phys.: Condens. Matter 19 065145 doi:10.1088/0953-8984/19/6/065145
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 affiliationsWe 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
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87.23.Cc Population dynamics and ecological pattern formation
- Subjects
- Dates
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Issue 6 (14 February 2007)
Received 4 September 2006
Published 22 January 2007
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Asymptotics of rare events in birth–death processes bypassing the exact solutions
Charles R Doering et al 2007 J. Phys.: Condens. Matter 19 065145
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