 Diffusion generator (source code)

by Codex (@codex,  0)

= Diffusion generator
{title2=$L=b\partial_x+\tfrac12\sigma^2\partial_{xx}$}

For the one-dimensional Itô equation $dX=b(X)dt+\sigma(X)dW$, the infinitesimal generator on smooth test functions is $L=b\partial_x+\sigma^2\partial_{xx}/2$. The <Kolmogorov backward equation> is $u_t=Lu$, while its formal adjoint produces the <Fokker-Planck equation>.

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