44 citations · 119 across the 10 of their papers we have counts for
8 papers · 1 filter
Maximal Inequalities and Some Applications
Franziska Kühn, René L. Schilling
A maximal inequality is an inequality which involves the (absolute) supremum or the running maximum of a stochastic process $(X_t)_{t\…
A Liouville theorem for Lévy generators
Franziska Kühn
Under mild assumptions, we establish a Liouville theorem for the "Laplace" equation associated with the infinitesimal generator of a Lévy process: If is a weak solut…
On infinitesimal generators of sublinear Markov semigroups
Franziska Kühn
We establish a Dynkin formula and a Courrège-von Waldenfels theorem for sublinear Markov semigroups. In particular, we show that any sublinear operator on $C_c^{\infty}(\mathbb…
Schauder estimates for Poisson equations associated with non-local Feller generators
Franziska Kühn
We show how Hölder estimates for Feller semigroups can be used to obtain regularity results for solutions to the Poisson equation associated with the (extended) infinitesima…
Strong convergence of the Euler--Maruyama approximation for a class of Lévy-driven SDEs
Franziska Kühn, René L. Schilling
Consider the following stochastic differential equation (SDE) driven by a -dimensional Lévy process . We est…
On Martingale Problems and Feller Processes
Franziska Kühn
Let be a pseudo-differential operator with negative definite symbol . In this paper we establish a sufficient condition such that the well-posedness of the $(A,C_c^{\infty}(…
On the domain of fractional Laplacians and related generators of Feller processes
Franziska Kühn, René L. Schilling
In this paper we study the domain of stable processes, stable-like processes and more general pseudo- and integro-differential operators which naturally arise both in analysis and…
Moderate deviations and Strassen's law for additive processes
Franziska Kühn, René L. Schilling
We establish a moderate deviation principle for processes with independent increments under certain growth conditions for the characteristics of the process. Using this moderate de…