43 citations · 66 across the 11 of their papers we have counts for
5 papers · 1 filter
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…
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…
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…