A comparison principle for large deviations

Abstract:

If $\{ {\mu _n}\}$ and $\left \{ {{\nu _n}} \right \}$ are two sequences of probability measures on a separable metric space, we give conditions under which $\left \{ {{\mu _n}} \right \}$ satisfies a large deviation principle if and only if $\left \{ {{\nu _n}} \right \}$ does. A known and a new theorem follow immediately from the application of this comparison principle to standard results in large deviation theory.