Reaction of water with silver nitrate

There is no reaction between Silver nitrate (AgNO3) and water (H2O). It is a physical process known as solvating of electrolyte. 

The only reaction that may be possible in the solution of AgNO3 
If the solution is not stored in umber bottle then silver ions when exposed to sunlight will turn solution into black colored. This is because silver ions react in sunlight to give metallic silver which is black in color