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As a model of Brownian motor, we consider the motion of particles in an asymmetric, single-well, periodic potential undergoing half-period shifts driven by two Poisson processes. Probability currents and stopping force are explicitly obtained as a function of the model parameters, and use of the notion of driving effective potential is made to bridge the present model with our previous works involving washboard potentials. [ABSTRACT FROM AUTHOR]

We consider a stochastic neuronal model in which the time evolution of the membrane potential is described by a Wiener process perturbed by random jumps driven by a counting process. We consider the first-crossing-time problem through a constant boundary for such a process, in order to describe the firing activity of the model neuron. We build up a new simulation procedure for the construction of firing densities estimates. [ABSTRACT FROM AUTHOR]

Motivated by a typical and well-known problem of neurobiological modeling, a parallel algorithm devised to simulate sample paths of stationary normal processes with rational spectral densities is implemented to evaluate first passage time probability densities for time-varying boundaries. After a self-contained outline of the original problem and of the involved computational framework, the results of numerous simulations are discussed and conclusions are drawn on the effect of a periodic boundary and a Butterworth-type covariance on determining quantitative and qualitative features of first passage time probability densities. [ABSTRACT FROM AUTHOR]