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As the noise in Eq. (5) is additive, standard integrators such as the Euler Maruyama method converge with mean-square order one.

end{aligned} (24) For (varSigma={mathbb{O}_{3}}), Eq. (24) is a second-order method for the deterministic Eq. (2), however, the mean-square order of Eq. (24) is still one.

To increase the mean-square order one has to include higher-order stochastic integrals to reproduce the interactions of the Subsystems (20a) and (20b) (see [50], Sect. 2, for details).

As expected, both methods have mean-square order one, however, for (C=135) the mean-square error (MSE) of the splitting method is significantly smaller than the MSE of the Euler Maruyama method.

Indeed Li [ 37] has shown that the Poisson τ-leap method has mean square strong order 1 2 and weak order 1 and this is consistent with the previous remarks.

OMP is based on an iterative procedure that calculates the least mean square in order to minimize the error and update residual.

The factors and interaction terms were compared to the Error MS (mean square) in order to assess their significance.

The response mean squares, fourth order moments, and fourth order cumulants are presented as functions of the internal resonance detuning for various system parameters.

This is true of any method of calculating reliability based on algebraically manipulating mean squares in order to obtain unbiased estimates of the sources of variance in the ratings.

Let (X t)) be a mean square differentiable second order stochastic process in (I=[t_{0},T]) and mean square continuous in it.

The TMD methodology imposes a time-dependent holonomic or harmonic constraint on the RMSD (root mean square deviation) in order to drive the system to a target structure.

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