In mathematics, exponential equivalence of measures is how two sequences or families of probability measures are "the same" from the point of view of large deviations theory.
be a metric space and consider two one-parameter families of probability measures on
ε
ε > 0
ε
ε > 0
These two families are said to be exponentially equivalent if there exist such that The two families of random variables
are also said to be exponentially equivalent.
The main use of exponential equivalence is that as far as large deviations principles are concerned, exponentially equivalent families of measures are indistinguishable.
More precisely, if a large deviations principle holds for
with good rate function
are exponentially equivalent, then the same large deviations principle holds for
with the same good rate function