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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2018

Paper 3

Define the <Multivariate Fokker-Planck probability current> by
$$
\boxed{J_i=A_iP-\frac12\frac{\partial}{\partial x_j}(B_{ij}P).}
$$
Then
$$
-\frac{\partial J_i}{\partial x_i}
=-\frac{\partial}{\partial x_i}(A_iP)
+\frac12\frac{\partial^2}{\partial x_i\partial x_j}(B_{ij}P),
$$
so the <Fokker-Planck equation> is exactly the <continuity equation> $\partial_tP+\nabla\cdot\mathbf J=0$.

Solution

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

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

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

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