A Markov chain model is constructed to investigate fluctuations in the mass of the zodiacal cloud. The cloud is specified by a three‐dimensional grid, each element of which contains the numbers of dust particles as a function of semimajor axis, eccentricity and mass. The evolutionary pathways of dust particles owing to radiation pressure are described by fixed transition probabilities connecting the grid elements. Other elements are absorbing states representing infall to the Sun or ejection to infinity: particles entering these states are removed from the system. Particles are injected through the breakup of comets entering short‐period, high‐eccentricity orbits at random times, and are subject to the Poynting–Robertson effect and removal through collisional disintegration and radiation pressure. The main conclusions are that the cometary component of the zodiacal cloud is highly variable, and that in the wake of giant comet entry into a short‐period, near‐Earth orbit, the dust influx to the Earth's atmosphere may acquire a climatically significant optical depth.