The significant advances in nonlinear stochastic dynamics and control in Hamiltonian formulation during the past decade are reviewed. The exact stationary solutions and equivalent nonlinear system method of Gaussian-white -noises excited and dissipated Hamiltonian systems, the stochastic averaging method for quasi Hamiltonian systems, the stochastic stability, stochastic bifurcation, first-passage time and nonlinear stochastic optimal control of quasi Hamiltonian systems are summarized. Possible extension and applications of the theory are pointed out. This review article cites 158 references.

Data availabilitySummary statistics generated by COVID-19 Host Genetics Initiative are available online (https://www.covid19hg.org/results/r6/). The analyses described here use the freeze 6 data. The COVID-19 Host Genetics Initiative continues to regularly release new data freezes. Summary statistics for samples from individuals of non-European ancestry are not currently available owing to the small individual sample sizes of these groups, but the results for 23 loci lead variants are reported in Supplementary Table 3. Individual-level data can be requested directly from the authors of the contributing studies, listed in Supplementary Table 1.

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