Approximations of Cumulants of the Stochastic Power Law Logistic Model

A manuscript with the above title was finished in February, 2018. The manuscript has been submitted for publication, but has so far (in August of 2018) not been accepted. Some of the numerical evaluations and formal derivations in this manuscript have used Maple, and can be found here.

Derivations of ODEs for the first 3 cumulants are described here.

Derivations of asymptotic approximations of the first 3 cumulants of the QSD for s=1 are given here.

Derivations of asymptotic approximations of the first 3 cumulants of the QSD for s=2 are given here.

Derivations of asymptotic approximations of the first 3 cumulants of the QSD for s=3 are given here.

Derivations of asymptotic approximations of the first 3 cumulants of the QSD for s=4 are given here.

Derivations of asymptotic approximations of the first 3 cumulants of the QSD for s=5 are given here.

Derivations of asymptotic approximations of the first 3 cumulants of the QSD for s=6 are given here.

Derivations of asymptotic approximations of the first 3 cumulants of the QSD for s=7 are given here.

Derivations of asymptotic approximations of the first 3 cumulants of the QSD for s=8 are given here.

Derivations of asymptotic approximations of the first 3 cumulants of the QSD for s=9 are given here.

Derivations of asymptotic approximations of the first 3 cumulants of the QSD for s=10 are given here.

Various numerical evaluations are shown here.

Some other methods with s=1 are studied here.

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