A multiscale stochastic criminal behavior model under a hybrid scheme
نویسندگان
چکیده
<p style='text-indent:20px;'>Crime in urban environment is a major social problem nowadays. As such, many efforts have been made to develop mathematical models for this type of crime. The pioneering work [M. B. Short, M. R. D'Orsogna, V. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and Chayes, Math. Models Methods Appl. Sci., 18, (2008), pp. 1249-1267] establishes an agent-based human-environment interaction model criminal behavior residential burglary, where aggregate pattern formation "hotspots" quantitatively studied the first time. Potential offenders are assumed interact with according well-known criminology sociology notions. However long-term simulations coupled dynamics computationally costly due all components evolving on slow time scales. In paper, we introduce new-generation separated spatio-temporal scales agent actions parameter reactions. computational cost reduced significantly, while essential stochastic features preserved. Moreover, separation brings into theoretical framework piecewise deterministic Markov processes (PDMP). A martingale approach applicable which will be useful analyze both statistical subsequent studies.</p>
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ژورنال
عنوان ژورنال: Electronic research archive
سال: 2021
ISSN: ['2688-1594']
DOI: https://doi.org/10.3934/era.2021011