<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 ...

Abstract We introduce a new class of continuous-time models the stochastic volatility asset prices. The can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized facts often found in data. Our prime model is based on so-called Brownian semistationary process we derive number theoretical properties this process, relevant t...