Measuring the intensity of the prevalence of radicalization plays a vital role in countering violent extremism. Hence, several mathematical models have been proposed aiming to describe the complex dynamics of this social phenomenon. It should be noted that existing literature mainly includes deterministic compartmental models, while the measuring of the extremism's intensity is based on the basic reproduction number R0. However, deterministic approaches can only provide an estimation of the mean tendency of the phenomenon, while the R0 index is accompanied by several drawbacks. In this paper, we propose a new compartmental scheme which considers control policies, containing susceptible, resistant, extremist and under-rehabilitation cases. The aforementioned model is combined with the methodology of continuous time Markov processes, leading to the quantification of not just the mean trend but the uncertainty of the phenomenon, too. Moreover, we introduce two new stochastic descriptors for the assessment of the radicalization's severity, namely the exact (Rε) and aggregate (Ra) reproduction numbers that address the limitation of the widely used R0 index. Emphasis is placed on the presentation of theorems and algorithms that describe the computation of their complete distribution functions. We derive formulas for the calculation of elasticities, and perform a perturbation analysis, shedding light on the overall impact of system's parameters on the selected stochastic descriptors. A series of illustrative examples is presented for the illustration of the derived theoretical properties, along with numerical comparisons between the three reproduction numbers. Finally, based on the proposed measures, we pinpoint the most impactful factors, and discuss control policies that facilitate the effective combating of the negative repercussions of terrorism.