  Our purpose is to obtain a very effective and general method to prove that
certain $C_0$-semigroups admit invariant strongly mixing measures. More
precisely, we show that the Frequent Hypercyclicity Criterion for
$C_0$-semigroups ensures the existence of invariant mixing measures with full
support. We will several examples, that range from birth-and-death models to
the Black-Scholes equation, which illustrate these results.
