79 citations · 575 across the 55 of their papers we have counts for
54 papers · 1 filter
Optimal Wasserstein- distance between SDEs driven by Brownian motion and stable processes
Changsong Deng, Rene L. Schilling, Lihu Xu
We are interested in the following two -valued stochastic differential equations (SDEs): \begin{gather*} d X_t=b(X_t)\,d t + σ\,d L_t, \quad X_0=x, %\label{BM-SDE} d…
The Liouville theorem for a class of Fourier multipliers and its connection to coupling
David Berger, René L. Schilling, Eugene Shargorodsky
The classical Liouville property says that all bounded harmonic functions in , i.e.\ all bounded functions satisfying , are constant. In this paper we obtain…
Analytical and computational problems related to fractional Gaussian noise
Yuliya Mishura, Kostiantyn Ralchenko, René L. Schilling
We study the projection of an element of fractional Gaussian noise onto its neighbouring elements. We prove some analytic results for the coefficients of this projection, in partic…
Approximation of the invariant measure of stable SDEs by an Euler--Maruyama scheme
Peng Chen, Changsong Deng, Rene Schilling +1
We propose two Euler-Maruyama (EM) type numerical schemes in order to approximate the invariant measure of a stochastic differential equation (SDE) driven by an -stable Lévy pro…
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\…
On -scale functions of spectrally negative Lévy processes
Anita Behme, David Oechsler, René L. Schilling
We obtain series expansions of the -scale functions of arbitrary spectrally negative Lévy processes, including processes with infinite jump activity, and use these to derive var…