Transition density
= Transition density
{title2=$P_t(x,dy)=p_t(x,y)\,dy$}
A <probability density function> for the conditional future state of a <Markov process> given its current state. Integrating $p_t(x,y)$ over a measurable region gives its <transition probability>. A <transition kernel> need not admit a density; discrete or partly atomic transition laws require a different reference measure or a separate atomic part.