Lévy kernel of a Markov jump process (source code)

= Lévy kernel of a Markov jump process
{c}
{title2=$K(x,dz)$}

A kernel specifying the jump rate from state $x$ for each displacement $z$. With the displacement convention the <infinitesimal generator> is $L\varphi(x)=\int(\varphi(x+z)-\varphi(x))K(x,dz)$. The destination convention instead records a rate measure on the new state, translating each displacement by $x$. For finite total rate, that total is the exponential holding rate and the normalized measure is the next-jump distribution.