Is there any evidence that the Gas Giant planets in our solar system are experiencing orbital migration? Planetary migration is defined by Lubow and Ida (2010) in their article Planet Migration as 


  the process by which a planet’s orbital radius changes in time. The
  main agent for causing gas giant planet migration is the gravitational interaction of the young
  planet with the gaseous disk from which it forms.


Relevant, it is believed by some that the gas giant planets in our solar system experienced orbital migration.  According to the article Wandering Gas Giants and Lunar Bombardment (Taylor, 2006), as an example,


  Outward migration of Saturn might have triggered a dramatic increase in the bombardment rate on the Moon 3.9 billion years ago, an idea testable with lunar samples.


So my question is is there any evidence (not opinions) to suggest any form of migration occurring with our solar system's gas giants?
There is no direct evidence of change of orbits of the gaseous planets of the Solar System. But one could wonder about the stability of the Solar System, and if such events could happen again.

Theory:

The Solar System is a chaotic system, as most of gravitational systems involving $N$ bodies. The KAM theorems (for Kolmogorov, Arnold and Moser, the three authors of the theory) show that, for non-degenerate Hamiltonian systems, quasiperiodic trajectories exist, that could ensure the stability of the system. But unfortunatly the KAM theorems cannot be applied to the Solar System, because the planets are too massive. 

Simulations:

It leaves us with numerical simulations, that show that the Solar System is indeed chaotic, and that planetary collisions, ejection and migration can happen. But if it is true for the telluric planets, it is not the case for the gaseous planets: one reason could be that they are not much perturbated by the inner planets.

Sources:


Laskar (1994)
Laskar (2012)