Compute the intermittency generating vector (16.19) [ varphi_{alpha}(mathbf{w} ; tau, Delta tau, mathbf{X})=frac{1}{sqrt{Sigma_{(alpha alpha)}}}leftlangleDelta A_{alpha} mid mathbf{W}=mathbf{w}

Question:

Compute the intermittency generating vector (16.19)

\[ \varphi_{\alpha}(\mathbf{w} ; \tau, \Delta \tau, \mathbf{X})=\frac{1}{\sqrt{\Sigma_{(\alpha \alpha)}}}\left\langle\Delta A_{\alpha} \mid \mathbf{W}=\mathbf{w}\rightangle-w_{\alpha}\left(\left\langle\triangle A_{(\alpha)} W_{(\alpha)}\rightangle-\left\langle\Delta A_{(\alpha)}\rightangle\left\langle W_{(\alpha)}\rightangle\right) \]

for non-degenerate Gaussian statistics.

Eq (16.19)

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