This article focuses only on one specialized aspect of the subject. Please help
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Typically,
differential equations describing the i-th moment will depend on the (i + 1)-st moment. To use moment closure, a level is chosen past which all
cumulants are set to zero. This leaves a resulting closed system of equations which can be solved for the moments.[1] The approximation is particularly useful in models with a very large
state space, such as stochastic
population models.[1]
History
The moment closure approximation was first used by Goodman[2] and Whittle[3][4] who set all third and higher-order cumulants to be zero, approximating the population distribution with a
normal distribution.[1]
In 2006, Singh and Hespanha proposed a closure which approximates the population distribution as a
log-normal distribution to describe biochemical reactions.[5]
^Whittle, P. (1957). "On the Use of the Normal Approximation in the Treatment of Stochastic Processes". Journal of the Royal Statistical Society. 19 (2): 268–281.
JSTOR2983819.
^Matis, J. H.; Kiffe, T. R. (1996). "On Approximating the Moments of the Equilibrium Distribution of a Stochastic Logistic Model". Biometrics. 52 (3): 980–991.
doi:
10.2307/2533059.
JSTOR2533059.
^Marion, G.; Renshaw, E.; Gibson, G. (1998). "Stochastic effects in a model of nematode infection in ruminants". Mathematical Medicine and Biology. 15 (2): 97.
doi:
10.1093/imammb/15.2.97.
^Baytaş, Bekir; Bojowald, Martin; Crowe, Sean (2018-12-17). "Canonical tunneling time in ionization experiments". Physical Review A. 98 (6). American Physical Society (APS): 063417.
arXiv:1810.12804.
doi:
10.1103/physreva.98.063417.
ISSN2469-9926.