The Spike Noise Based on the Renewal Point Process and Its Possible Applications

2010

We consider a non-Markovian random process in the form of spikes train, where the time intervals between neighboring delta-pulses are mutually independent and identically distributed, i.e. represent the renewal process (1967). This noise can be interpreted as the derivative of well-known continuous time random walk (CTRW) model process with fixed value of jumps. The closed set of equations for the characteristic functional of the noise, useful to split the correlations between stochastic functionals (2008), is obtained. In the particular case of Poisson statistics these equations can be exactly solved and the expression for the characteristic functional coincides with the result for shot no…