43 citations · 66 across the 11 of their papers we have counts for
12 papers
Benjamini-Schramm limit of the heat semigroup on quantum graphs
Mihály Kovács, Eszter Sikolya
We study the behaviour of heat semigroups on quantum graphs under Benjamini-Schramm convergence. For quantum graphs with uniformly bounded geometry, equipped with continuity and Ki…
Journey Through the World of Dynamical Systems on Networks
A. Puchalska, M. N. Cartier van Dissel, P. Gora +9
We present a subjective selection of methods for complex systems analysis ranging from statistical tools through numerical methods based on AI to both linear and non-linear ODEs an…
On the strong Feller property of the heat equation on quantum graphs with Kirchoff noise
Mohamed Fkirine, Mihály Kovács, Eszter Sikolya
We consider a so-called quantum graph with standard continuity and Kirchhoff vertex conditions where the Kirchhoff vertex condition is perturbed by Gaussian noise. We show that the…
Reaction-diffusion equations on metric graphs with edge noise
Eszter Sikolya
We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equa…
On the parabolic Cauchy problem for quantum graphs with vertex noise
Mihály Kovács, Eszter Sikolya
We investigate the parabolic Cauchy problem associated with quantum graphs including Lipschitz or polynomial type nonlinearities and additive Gaussian noise perturbed vertex condit…
Stochastic reaction-diffusion equations on networks
Mihály Kovács, Eszter Sikolya
We consider stochastic reaction-diffusion equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative cylindrical Gaussian noise driven…
On the stochastic Allen-Cahn equation on networks with multiplicative noise
Mihály Kovács, Eszter Sikolya
We consider a system of stochastic Allen-Cahn equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative Gaussian noise driven stochast…
Ornstein-Uhlenbeck approximation of one-step processes: a differential equation approach
Peter L. Simon, Eszter Sikolya
The steady state of the Fokker-Planck equation corresponding to a density dependent one-step process is approximated by a suitable normal distribution. Starting from the master equ…
Semigroups of max-plus linear operators
Marjeta Kramar Fijavž, Aljoša Peperko, Eszter Sikolya
We define strongly continuous max-additive and max-plus linear operator semigroups and study their main properties. We present some important examples of such semigroups coming fro…
Variational and Semigroup Methods for Waves and Diffusion in Networks
Marjeta Kramar Fijavz, Delio Mugnolo, and Eszter Sikolya
We study diffusion and wave equations in networks. Combining semigroup and variational methods we obtain well-posedness and many nice properties of the solutions in general L^p -co…
Differential equation approximations of stochastic network processes: an operator semigroup approach
András Bátkai, Istvan Z. Kiss, Eszter Sikolya +1
The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by…
The norm convergence of a Magnus expansion method
András Bátkai, Eszter Sikolya
We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method will be investigated.