18 citations · 50 across the 15 of their papers we have counts for
16 papers
Fast-slow chemical reactions: convergence of Hamilton-Jacobi equation and variational representation
Yuan Gao, Artur Stephan
Microscopic behaviors of chemical reactions can be described by a random time-changed Poisson process, whose large-volume limit determines the macroscopic behaviors of species conc…
On time-splitting methods for gradient flows with two dissipation mechanisms
Alexander Mielke, Riccarda Rossi, Artur Stephan
We consider generalized gradient systems in Banach spaces whose evolutions are generated by the interplay between an energy functional and a dissipation potential. We focus on the…
Trotter-type formula for operator semigroups on product spaces
Artur Stephan
We consider a Trotter-type-product formula for approximating the solution of a linear abstract Cauchy problem (given by a strongly continuous semigroup), where the underlying Banac…
Positivity and polynomial decay of energies for square-field operators
Artur Stephan, Holger Stephan
We show that for a general Markov generator the associated square-field (or carré du champs) operator and all their iterations are positive. The proof is based on an interpolation…
Coarse-graining and reconstruction for Markov matrices
Artur Stephan
We present a coarse-graining (or model order reduction) procedure for stochastic matrices by clustering. The method is consistent with the natural structure of Markov theory, prese…
EDP-convergence for a linear reaction-diffusion system with fast reversible reaction
Artur Stephan
We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two diffusion equations coupled by a linear reaction. We understand the linear reaction-diffus…
EDP-convergence for nonlinear fast-slow reaction systems with detailed balance
Alexander Mielke, Mark A. Peletier, Artur Stephan
We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with L…
Consistency and convergence for a family of finite volume discretizations of the Fokker--Planck operator
Martin Heida, Markus Kantner, Artur Stephan
We introduce a family of various finite volume discretization schemes for the Fokker--Planck operator, which are characterized by different weight functions on the edges. This fami…
Operator-Norm Convergence of the Trotter Product Formula on Hilbert and Banach Spaces: A Short Survey
Hagen Neidhardt, Artur Stephan, Valentin Zagrebnov
We give a review of results on the operator-norm convergence of the Trotter product formula on Hilbert and Banach spaces, which is focused on the problem of its convergence rates.…
Coarse-graining via EDP-convergence for linear fast-slow reaction systems
Alexander Mielke, Artur Stephan
We consider linear reaction systems with slow and fast reactions, which can be interpreted as master equations or Kolmogorov forward equations for Markov processes on a finite stat…
Combinatorial considerations on the invariant measure of a stochastic matrix
Artur Stephan
The invariant measure is a fundamental object in the theory of Markov processes. In finite dimensions a Markov process is defined by transition rates of the corresponding stochasti…
Trotter product formula and linear evolution equations on Hilbert spaces On the occasion of the 100th birthday of Tosio Kato
Hagen Neidhardt, Artur Stephan, Valentin Zagrebnov
The paper is devoted to evolution equations of the form t u(t) = --(A + B(t))u(t), t I = [0, T ], on separable Hilbert spaces where A is a non-negative s…
Memory equations as reduced Markov processes
Artur Stephan, Holger Stephan
A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov…
Remarks on the operator-norm convergence of the Trotter product formula
Hagen Neidhardt, Artur Stephan, Valentin A. Zagrebnov
We revise the operator-norm convergence of the Trotter product formula for a pair {A,B} of generators of semigroups on a Banach space. Operator-norm convergence holds true if the d…
Phase response function for oscillators with strong forcing or coupling
Vladimir Klinshov, Serhiy Yanchuk, Artur Stephan +1
Phase response curve (PRC) is an extremely useful tool for studying the response of oscillatory systems, e.g. neurons, to sparse or weak stimulation. Here we develop a framework fo…
Convergence rate estimates for Trotter product approximations of solution operators for non-autonomous Cauchy problems
Hagen Neidhardt, Artur Stephan, Valentin A. Zagrebnov
In the present paper we advocate the Howland-Evans approach to solution of the abstract non-autonomous Cauchy problem (non-ACP) in a separable Banach space X. The main idea is to r…