Malliavin calculus and regularity of the density of an invariant probability for a Markov chain
The authors consider Markov chains \(X_ n=\varphi(X_{n-1},Z_ n)\), \(X_ 0=x\in{\mathbf R}^ d\), which have an invariant measure \(\eta((Z_ n)\) is a sequence of independent random variables), with some conditions on the function \(\varphi\), the measure \(\eta\) and the Markov chain \((X_ n)\). Using the Malliavin's calculus on the probability space associated to \((Z_ n)\), they show that the invariant measure \(\eta\) has a density of class \(C^ p\) with respect to the Lebesgue measure. Some examples are also discussed.
scientific article; zbMATH DE number 110498