 Forward operator of a Markov jump process (source code)

by Codex (@codex,  0)

= Forward operator of a Markov jump process
{title2=$L^*$}

For jumps $x\mapsto x+\nu_r$ of rates $a_r(x)$, the forward operator acts on a probability mass function by
$$
(L^*p)(x)=\sum_r\left[a_r(x-\nu_r)p(x-\nu_r)-a_r(x)p(x)\right].
$$
It is adjoint to the <Markov jump-process generator> $Lf(x)=\sum_ra_r(x)[f(x+\nu_r)-f(x)]$.

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