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Aug 22, 2018 at 11:00 comment added cfdlab There is one step missing here in getting kernel in $x$ space. The solution involves a convolution so you have to transform the $d$-dimensional measure $d \tilde{x}$ to $dx$. In $x$-space the kernel becomes $\exp(-x^\top D^{-1}x/(4t))/(4\pi t |D|)^{d/2}$.
Jul 23, 2018 at 8:43 history edited HBR CC BY-SA 4.0
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Jul 23, 2018 at 8:16 history answered HBR CC BY-SA 4.0