Anita Behme, Alexander Schnurr
Published 2013-10-16, updated 2015-07-28Version 3
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.
Comments: Published at http://dx.doi.org/10.3150/14-BEJ618 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
Journal: Bernoulli 2015, Vol. 21, No. 3, 1697-1718
On ergodicity of some Markov processes
Invariant measure for the stochastic Cauchy problem driven by a cylindrical Lévy process
Characterization of the convergence in total variation and extension of the Fourth Moment Theorem to invariant measures of diffusions
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