= Gaussian white-noise magnetic stretching
{title2=$\dot B_i=\sigma_{im}B_m$}
For a trace-free isotropic <Gaussian white noise> velocity gradient with covariance $\langle\sigma_{im}(t)\sigma_{jn}(t')\rangle=\kappa_2\delta(t-t')[\delta_{ij}\delta_{mn}-(\delta_{im}\delta_{jn}+\delta_{in}\delta_{jm})/4]$, interpret the multiplicative equation as the <Stratonovich integral> limit of smooth velocity fluctuations. The causal <Furutsu–Novikov formula> has endpoint weight one half. It gives $P_t=(\kappa_2/2)\partial_i[(B^2\delta_{ij}-B_iB_j/2)\partial_jP]$ for the vector <probability density function>.
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