TY - JOUR
T1 - An alternative route to the system-size expansion
AU - Cianci,Claudia
AU - Schnoerr,David
AU - Piehler,Andreas
AU - Grima,Ramon
N1 - David Schnoerr funded by BBSRC BB/F017073/1
PY - 2017/9/4
Y1 - 2017/9/4
N2 - The master equation is rarely exactly solvable and hence various means of approximation have been devised. A popular systematic approximation method is the system-size expansion which approximates the master equation by a generalised Fokker-Planck equation. Here we first review the use of the expansion by applying it to a simple chemical system. The example shows that the solution of the generalised Fokker-Planck equation obtained from the expansion is generally not positive definite and hence cannot be interpreted as a probability density function. Based on this observation, one may also a priori conclude that moments calculated from the solution of the generalised Fokker-Planck equation are not accurate; however calculation shows these moments to be in good agreement with those obtained from the exact solution of the master equation. We present an alternative simpler derivation which directly leads to the same moments as the system-size expansion but which bypasses the use of generalised Fokker-Planck equations, thus circumventing the problem with the probabilistic interpretation of the solution of these equations.
AB - The master equation is rarely exactly solvable and hence various means of approximation have been devised. A popular systematic approximation method is the system-size expansion which approximates the master equation by a generalised Fokker-Planck equation. Here we first review the use of the expansion by applying it to a simple chemical system. The example shows that the solution of the generalised Fokker-Planck equation obtained from the expansion is generally not positive definite and hence cannot be interpreted as a probability density function. Based on this observation, one may also a priori conclude that moments calculated from the solution of the generalised Fokker-Planck equation are not accurate; however calculation shows these moments to be in good agreement with those obtained from the exact solution of the master equation. We present an alternative simpler derivation which directly leads to the same moments as the system-size expansion but which bypasses the use of generalised Fokker-Planck equations, thus circumventing the problem with the probabilistic interpretation of the solution of these equations.
KW - master equations
KW - stochastic
KW - system-size expansion
UR - http://www.scopus.com/inward/record.url?scp=85028961420&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/aa85aa
DO - 10.1088/1751-8121/aa85aa
M3 - Article
VL - 50
JO - Journal of Physics A: Mathematical and Theoretical
T2 - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 39
M1 - 395003
ER -