Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 13C / a / Solution

{c}
{title2=$J_i$}

For
$$
\partial_tP=-\partial_i(A_iP)+\frac12\partial_i\partial_j(B_{ij}P),
$$
the probability current is
$$
J_i=A_iP-\frac12\partial_j(B_{ij}P),
$$
so the equation is the continuity equation $\partial_tP+\partial_iJ_i=0$.


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 Incoming links: Multivariate Fokker-Planck probability current