Some inequalities with integral means.
Remarks on Voronovskaya's theorem.
Inequalities involving the inner product.
Lipschitz Contractions, Unique Ergodicity and Asymptotics of Markov Semigroups
We are mainly concerned with the asymptotic behaviour of both discrete and continuous semigroups of Markov operators acting on the space of all continuous functions on a compact metric space . We establish a simple criterion under which such semigroups admit a unique invariant probability measure on that determines their limit behaviour on and on . The criterion involves the behaviour of the semigroups on Lipschitz continuous functions and on the relevant Lipschitz seminorms. Finally,...
Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator
The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the...
Asymptotic behaviour of differentiated Bernstein polynomials
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