ИСТИНА

Random pulse processes with regulated periodicity, such as Dead-time-distorted Poisson pulse noise and Pulse process with fixed time intervals, are widely used for modeling noise-induced effects. They are used from stochastic thermodynamics, nanotechnology, electronics to population dynamics and epidemiology. Experimental and computational studies presented in the literature have explored the similarities in the behavior of these systems. We present a new stochastic process consisting of delta pulses with periodical magnitude, which is suitable to be treated both analytically and by numerical approach. This Poisson process is characterized by a time interval between two successive pulses. This random quantity has a mean value which coincides with the quasi-period of the Poisson process. The ratio of period of amplitude modulation and the quasi-period of the pulses can be called parameter of periodicity. The more the parameter of periodicity the more correlated the process. This process is suitable to obtain noise sources with varying degree of randomness, ranging from white noise, to quasi-periodical process. Spectral density and correlation function can be calculated analytically for the case of harmonically modulated pulses. Correlation time increases with the parameter of periodicity. This process can be used as noise source in stochastic differential equations describing fluctuating parameters in physics and biology. The dependance of moments on noise periodicity in not trivial. For population dynamics and epidemiology this model helps to take into account the influence of seasonal changing of environment on some unpredictable events, such as huge increases of a population, epidemics, and other ecological problems. Here the period corresponds to year. It is known that some random mutations are useful at one season and dangerous at another. The same is for some anthropogenic influences. For example, warming after a technogenic accident can be good for population in winter and lethal in summer. Parameter of periodicity can be used as criterium to distinguish quantum and classical optics. If the quasi-period of the pulses is average time between photons registration and period is inverse frequency of light, than the condition of small parameter of periodicity is equivalent to condition that light intensity is much less than Planck constant. This noise can be used for description of acceleration of billiard particle by periodically moving scatterers. Correlation time of this process is estimated to prove applicability of Fokker-Planck equation for velocity distribution and calculate Fermi acceleration.