## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Foundations of Data Science
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

NHM

Differential equation approximations of stochastic network processes: An operator semigroup approach

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 its master
equation, which is a system of linear ODEs with large state space size ($N$). We derive a single
non-linear ODE (called mean-field approximation) for the expected value that yields a good
approximation as $N$ tends to infinity. Using only elementary semigroup theory we can prove the order $\mathcal{O}(1/N)$ convergence of the solution of the system to that of the mean-field equation. The proof
holds also for cases that are somewhat more general than the usual density dependent one. Moreover, for
Markov chains where the transition rates satisfy some sign conditions, a new approach using a countable system of ODEs for proving
convergence to the mean-field limit is proposed.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]