The study of neuronal bursting activity, observed in cell-culture, is physiologically important because is correlated with synaptic transmission, plasticity, and information processing. However, besides strong ethical issues related to the use of animal models, there are many limitations due to experimental setup and neural signaling acquisition. In this study, we propose a stochastic modeling approach to simulate neural dynamics observed in networks of neocortical neurons from an ex vivo normal mouse. Specifically, we devised a stochastic version of the Izhichevich's model of cortical neurons, and simulated a network of excitatory and inhibitory neurons also accounting for cell signaling delays. No specific learning rules were used throughout the simulation time. Results show spontaneous bursting activity while mimicking balanced and hyper-excitable networks through modulation of the inhibitory synaptic weights. Furthermore, we validate our findings comparing the simulated cumulative probability functions of the firing spike histograms with the ones obtained in cultured networks of dissociated cortical neurons from ex vivo mice.