Simulation of a diffusion process with randomly distributed jumps in neuronal context

In stochastic neuronal models, an interspike interval corresponds to the time interval during which the process imitating the membrane potential reaches a threshold from an initial depolarization. For neurons with an extensive dendritic structure, a stochastic process combining diffusion and discontinuous development of its trajectory is considered a good description of the membrane potential. Due to a lack of analytical solutions of the threshold passage distribution for such a process, a method for computer simulation is introduced here. For the diffusion Ornstein-Uhlenbeck process with exponentially distributed moments of constant jumps a program is given. The relation between the simulation step, accuracy of simulation and amount of computing time required is discussed.