We present a simple and general framework to simulate statistically correct
realizations for a system of non-Markovian discrete stochastic processes. We
give the exact analytical solution and a practical an efficient algorithm alike
the Gillespie algorithm for Markovian processes, with the difference that now
the occurrence rates of the events are stochastic processes themselves. We use
our non-Markovian stochastic simulation methodology to investigate the effects
of non-exponential inter-event time distributions in two case studies, the
susceptible-infected-susceptible model of epidemic spreading and biochemical
reactions with time delays. Strikingly, our results unveil the drastic effects
that very subtle differences in the modeling of non-Markovian processes have on
the global behavior of complex systems, with important implications for their
understanding and prediction.
%0 Journal Article
%1 Boguna2014Simulating
%A Bogu\ ná, Marian
%A Lafuerza, Luis F.
%A Toral, Raúl
%A Serrano, M. Ángeles
%D 2014
%J Physical Review E
%K gillespie, mc-simulations, sync-updates algorithms epidemic-models sis
%N 4
%R 10.1103/PhysRevE.90.042108
%T Simulating non-Markovian stochastic processes
%U http://dx.doi.org/10.1103/PhysRevE.90.042108
%V 90
%X We present a simple and general framework to simulate statistically correct
realizations for a system of non-Markovian discrete stochastic processes. We
give the exact analytical solution and a practical an efficient algorithm alike
the Gillespie algorithm for Markovian processes, with the difference that now
the occurrence rates of the events are stochastic processes themselves. We use
our non-Markovian stochastic simulation methodology to investigate the effects
of non-exponential inter-event time distributions in two case studies, the
susceptible-infected-susceptible model of epidemic spreading and biochemical
reactions with time delays. Strikingly, our results unveil the drastic effects
that very subtle differences in the modeling of non-Markovian processes have on
the global behavior of complex systems, with important implications for their
understanding and prediction.
@article{Boguna2014Simulating,
abstract = {{We present a simple and general framework to simulate statistically correct
realizations for a system of non-Markovian discrete stochastic processes. We
give the exact analytical solution and a practical an efficient algorithm alike
the Gillespie algorithm for Markovian processes, with the difference that now
the occurrence rates of the events are stochastic processes themselves. We use
our non-Markovian stochastic simulation methodology to investigate the effects
of non-exponential inter-event time distributions in two case studies, the
susceptible-infected-susceptible model of epidemic spreading and biochemical
reactions with time delays. Strikingly, our results unveil the drastic effects
that very subtle differences in the modeling of non-Markovian processes have on
the global behavior of complex systems, with important implications for their
understanding and prediction.}},
added-at = {2019-06-10T14:53:09.000+0200},
archiveprefix = {arXiv},
author = {Bogu\ {n}\'{a}, Marian and Lafuerza, Luis F. and Toral, Ra\'{u}l and Serrano, M. \'{A}ngeles},
biburl = {https://www.bibsonomy.org/bibtex/2c3506d77cd8e5b0683676acc44ac1443/nonancourt},
citeulike-article-id = {12934826},
citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.90.042108},
citeulike-linkout-1 = {http://arxiv.org/abs/1310.0926},
citeulike-linkout-2 = {http://arxiv.org/pdf/1310.0926},
day = 6,
doi = {10.1103/PhysRevE.90.042108},
eprint = {1310.0926},
interhash = {9d10246f917bb7d74db9a3e13474f58f},
intrahash = {c3506d77cd8e5b0683676acc44ac1443},
issn = {1550-2376},
journal = {Physical Review E},
keywords = {gillespie, mc-simulations, sync-updates algorithms epidemic-models sis},
month = oct,
number = 4,
posted-at = {2014-01-23 10:13:50},
priority = {2},
timestamp = {2019-08-22T16:24:38.000+0200},
title = {{Simulating non-Markovian stochastic processes}},
url = {http://dx.doi.org/10.1103/PhysRevE.90.042108},
volume = 90,
year = 2014
}