A criterion for invariant measures of Ito processes based on the symbol

作者：Behme Anita^*; Schnurr Alexander

来源：Bernoulli, 2015, 21(3): 1697-1718.

DOI：10.3150/14-BEJ618

• Feller process
• invariant measure
• Ito process
• Levy-type process
• stationarity
• stochastic differential equation
• symbol

An integral criterion for the existence of an invariant measure of an Ito process is developed. This new criterion is based on the probabilistic symbol of the Ito 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.

• 出版日期2015-8