A quasi likelihood for integral data on birth and death on flows

Birth and Death on a flow refers to a particle system on a stochastic flow. Particles are born in a point process and move on the flow subject to position-dependent killing. They die eventually and leave the flow. The particle process is a measure-valued, Markov process tracking these motions. Its law depends on the distribution of births, the coefficients of the flow, and the rate of killing. We parametrize the system and derive a quasi-likelihood for chronicles of integral data on the particle process.