A recent study shows that Jupiter most likely did migrate inward toward the sun, much like the "Hot Jupiters" found orbiting stars outside our own solar system.

A group of asteroids, known as the Hilda Asteroids, orbit the sun every eight years, as opposed to Jupiter's twelve year orbit.
Additionally, these particular asteroids have highly elliptic (oval-shaped) orbits, as opposed to most asteroids, the orbits of which are nearly circular.

According to scientists at the Harvard-Smithonian Center for astrophysics, Jupiter's gravity may have altered the orbit of these asteroids. Phil Armitage of the University of Colorado at Boulder adds: "“This is the first clear evidence I’ve seen for the migration of Jupiter.” He adds that Jupiter’s short trek could have disturbed the gravity of the bodies of the inner solar system so that they collided more frequently, spurring the formation and growth of our own Earth."