84 citations · 987 across the 100 of their papers we have counts for
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Strong Feller semigroups and Markov processes: A counter example
Lucian Beznea, Iulian Cîmpean, Michael Röckner
The aim of this note is to show, by providing an elementary way to construct counter-examples, that the strong Feller and the joint (space-time) continuity for a semigroup of Marko…
On nonlinear Markov processes in the sense of McKean
Marco Rehmeier, Michael Röckner
We study nonlinear time-inhomogeneous Markov processes in the sense of McKean's seminal work [32]. These are given as families of laws , , on path space,…
Path continuity of Markov processes and locality of Kolmogorov operators
Lucian Beznea, Iulian Cîmpean, Michael Röckner
We prove that if we are given a generator of a cadlag Markov process and an open domain in the state space, on which the generator has the local property expressed in a suitabl…
A Markov process for a continuum infinite particle system with attraction
Yuri Kozitsky, Michael Röckner
An infinite system of point particles placed in $\mathds{R}^d$ is studied. The particles are of two types; they perform random walks in the course of which those of distinct types…
Well-posedness of stochastic partial differential equations with fully local monotone coefficients
Michael Röckner, Shijie Shang, Tusheng Zhang
Consider stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple : \begin{align*} \left\{ \begin{al…
Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions
Zimo Hao, Michael Röckner, Xicheng Zhang
In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular -interactions as well as for the moderat…