Stochastic differential equations white noise

This white noise perturbance can be derived from a Wiener process W, and X then satisfies the stochastic differential equation... 

The Wiener process represents one possible form of diffusion processes. It is actually the integral of what in practical applications is called a white noise. The Wiener process with drift will be used in our application. The initial mean value (drift) is p and standard deviations for each time increment have been previously calculated—see Table 1. For our model we apply Wiener process with drift given by stochastic differential equation. 

When F(t) arises as a vector of Gaussian white noise process or as a vector of filtered white noise processes, it becomes advantageous to interpret Eq. 1 as an Ito s stochastic differential equation (SDE) and represent it as... 

The Stratonovich interpretation of Eq. (2.238) may also be obtained [31,32] from the white-noise limit of a sequence of stochastic ordinary differential equations (ODEs) of the form... 

The components of the excitation vector f t) are modeled as statistically independent stochastic processes defined as filtered white noise. Each component fj t) is defined as (t) = P]J u t), where j is a constant vector, and u t) denotes the state-vector of the filter which satisfies a first-order differential equation of the form... 

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