The origin of planetary impactors in the inner solar system
  New insights into the history of the inner solar system are derived from the impact cratering record of the Moon, Mars, Venus and Mercury, and from the size distributions of asteroid populations. Old craters from a unique period of heavy bombardment that ended $\sim$3.8 billion years ago were made by asteroids that were dynamically ejected from the main asteroid belt, possibly due to the orbital migration of the giant planets. The impactors of the past $\sim$3.8 billion years have a size distribution quite different from the main belt asteroids, but very similar to the population of near-Earth asteroids. 
Robert G. Strom, Renu Malhotra, Takashi Ito, Fumi Yoshida, David A.   Kring