Transient tracers and birth and death on flows: Parametric estimation of rates of drift, injection, and decay

Transient tracers refer to particulate matter in transport on fluid flows. We consider a stochastic description of such tracers in a model of birth and death on Brownian hows. 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. The mean of this system satisfies an advection-dispersion equation that describes the spatial evolution of tracer concentrations. It depends on the rate of drift on the flow, injection of new particles, and removal or decay. We derive likelihood, score, and information processes for parametric estimation of these rates from chronicles of tracer concentrations.