A criterion for invariant measures of It\^(o) processes based on the symbol

An integral criterion for the existence of an invariant measure of an It\^{o} process is developed. This new criterion is based on the probabilistic symbol of the It\^{o} process. In contrast to the standard integral criterion for invariant measures of Markov processes based on the generator, no test functions and hence no information on the domain of the generator is needed.