TY - JOUR
T1 - Asymptotics of rare events in birth-death processes bypassing the exact solutions
AU - Doering, Charles R.
AU - Sargsyan, Khachik V.
AU - Sander, Leonard M.
AU - Vanden-Eijnden, Eric
PY - 2007/2/14
Y1 - 2007/2/14
N2 - 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.
AB - 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.
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U2 - 10.1088/0953-8984/19/6/065145
DO - 10.1088/0953-8984/19/6/065145
M3 - Article
AN - SCOPUS:33947597442
SN - 0953-8984
VL - 19
JO - Journal of Physics Condensed Matter
JF - Journal of Physics Condensed Matter
IS - 6
M1 - 065145
ER -