Stochastic bursting in networks of excitable units with delayed coupling

We investigate the phenomenon of stochastic bursting in a noisy excitable unit with multiple weak delay feedbacks, by virtue of a directed tree lattice model. We find statistical properties of the appearing sequence of spikes and expressions for the power spectral density. This simple model is extended to a network of three units with delayed coupling of a star type. We find the power spectral density of each unit and the cross-spectral density between any two units. The basic assumptions behind the analytical approach are the separation of timescales, allowing for a description of the spike train as a point process, and weakness of coupling, allowing for a representation of the action of overlapped spikes via the sum of the one-spike excitation probabilities.

EFFICIENT PIECEWISE TREES FOR THE GENERALIZED SKEW VASICEK MODEL WITH DISCONTINUOUS DRIFT

In this paper, we explore two new tree lattice methods, the piecewise binomial tree and the piecewise trinomial tree for both the bond prices and European/American bond option prices assuming that the short rate is given by a generalized skew Vasicek model with discontinuous drift coefficient. These methods build nonuniform jump size piecewise binomial/trinomial tree based on a tractable piecewise process, which is derived from the original process according to a transform. Numerical experiments of bonds and European/American bond options show that our approaches are efficient as well as reveal several price features of our model.