Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Active Particles, Volume 2A Stochastic-Statistical Residential Burglary Model with Finite Size Effects

Active Particles, Volume 2: A Stochastic-Statistical Residential Burglary Model with Finite Size... [Transience of spatio-temporal clusters of residential burglary is well documented in empirical observations, and could be due to finite size effects anecdotally. However a theoretical understanding has been lacking. The existing agent-based statistical models of criminal behavior for residential burglary assume deterministic-time steps for arrivals of events. To incorporate random arrivals, this article introduces a Poisson clock into the model of residential burglaries, which could set time increments as independently exponentially distributed random variables. We apply the Poisson clock into the seminal deterministic-time-step model in Short et al. (Math Models Methods Appl Sci 18:1249–1267, 2008). Introduction of the Poisson clock not only produces similar simulation output, but also brings in theoretically the mathematical framework of the Markov pure jump processes, e.g., a martingale approach. The martingale formula leads to a continuum equation that coincides with a well-known mean-field continuum limit. Moreover, the martingale formulation together with statistics quantifying the relevant pattern formation leads to a theoretical explanation of the finite size effects. Our conjecture is supported by numerical simulations.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Active Particles, Volume 2A Stochastic-Statistical Residential Burglary Model with Finite Size Effects

Part of the Modeling and Simulation in Science, Engineering and Technology Book Series
Editors: Bellomo, Nicola; Degond, Pierre; Tadmor, Eitan
Wang, Chuntian; Zhang, Yuan; Bertozzi, Andrea L.; Short, Martin B.
Active Particles, Volume 2 — Aug 23, 2019
Download PDF
29 pages

Loading next page...
 
/lp/springer-journals/active-particles-volume-2-a-stochastic-statistical-residential-4q9XgJJRTv
Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2019
ISBN
978-3-030-20296-5
Pages
245 –274
DOI
10.1007/978-3-030-20297-2_8
Publisher site
See Chapter on Publisher Site

Abstract

[Transience of spatio-temporal clusters of residential burglary is well documented in empirical observations, and could be due to finite size effects anecdotally. However a theoretical understanding has been lacking. The existing agent-based statistical models of criminal behavior for residential burglary assume deterministic-time steps for arrivals of events. To incorporate random arrivals, this article introduces a Poisson clock into the model of residential burglaries, which could set time increments as independently exponentially distributed random variables. We apply the Poisson clock into the seminal deterministic-time-step model in Short et al. (Math Models Methods Appl Sci 18:1249–1267, 2008). Introduction of the Poisson clock not only produces similar simulation output, but also brings in theoretically the mathematical framework of the Markov pure jump processes, e.g., a martingale approach. The martingale formula leads to a continuum equation that coincides with a well-known mean-field continuum limit. Moreover, the martingale formulation together with statistics quantifying the relevant pattern formation leads to a theoretical explanation of the finite size effects. Our conjecture is supported by numerical simulations.]

Published: Aug 23, 2019

There are no references for this article.