Perfect Simulation for the Loss Network Point Process

The file perfect_simulation.py implements a class responsible to perform the perfect simulation for the Loss Network Point Process.

The file persistent_homology_perfect_simulatio.py implemets an exemple on how to use the class described above. The output is the persistent homology obtained from the point process of the invariant measure, calculated on the interval $I=[a, b] \subseteq \mathbb{R}$, from perfect_simulation.py.

References

1. Nancy L. Garcia, Nevena Maric, Improved bounds for perfect simulation of a continuous one-dimensional loss network, 2018 (arXiv)

2. Fernández, R., Ferrari, P. A., Garcia, N. L., Perfect simulation for interacting point processes, loss networks and Ising models, Stoch. Process. Appl, 102(1): 63-88, 2002.

3. Steve Y. Oudot, Persistence Theroy: From Quiver Representations to Data Analysis, Editora American Mathematical Society, 1º edition, 2016