A320 flight crew experienced left aft cockpit window cracking at FL310. After complying with QRH procedures they continue to their destination.

Narrative

In cruise flight; with no warning; a very loud 'crash' sounded behind me to my left. Upon turning around; I and the First Officer observed the rear window completely shattered. I and he immediately went on O2 and rechecked sear-belt integrity. I subsequently got an immediate decent to FL190 at which time we complied with QRH procedures and lowered delta-P to 4.8 PSI. The inner pane of glass was found to be completely intact. An anti-ice ECAM had appeared after the fact which we complied with as well. Seat belt sign was immediately put on and I made a PA to have Flight Attendant's cease service and buckle-up. Once established at FL190; I allowed Flight Attendant's to unbuckle but not serve. Seat belt sign was left on to landing as a precaution. We were later given an altitude restriction which we were going to be very tight on as we started down late. We were given a heading and a new altitude with a change of Centers. [There] appeared to be no conflicts. Attention to the window and current operations led to the late departure from FL190 to 12;000 FT. We probably would have made the restriction; but I informed Center as a precaution. [There was an] anti-ice malfunction on that window.