  We demonstrate that centered likelihood ratio estimators for the sensitivity
indices of complex stochastic dynamics are highly efficient with low, constant
in time variance and consequently they are suitable for sensitivity analysis in
long-time and steady-state regimes. These estimators rely on a new covariance
formulation of the likelihood ratio that includes as a submatrix a Fisher
Information Matrix for stochastic dynamics and can also be used for fast
screening of insensitive parameters and parameter combinations. The proposed
methods are applicable to broad classes of stochastic dynamics such as chemical
reaction networks, Langevin-type equations and stochastic models in finance,
including systems with a high dimensional parameter space and/or disparate
decorrelation times between different observables. Furthermore, they are simple
to implement as a standard observable in any existing simulation algorithms
without additional modifications.
