Effect of multiplicative noise on stationary stochastic process

Abstract

An open system that can be analyzed using the Langevin equation with multiplicative noise is considered. The stationary state of the system results from a balance of deterministic damping and random pumping simulated as noise with controlled periodicity. The dependence of statistical moments of the variable that characterizes the system on parameters of the problem is studied. A nontrivial decrease in the mean value of the main variable with an increase in noise stochasticity is revealed. Applications of the results in several physical, chemical, biological, and technical problems of natural and humanitarian sciences are discussed.

The correlation parameter of renewal processes and structures with positive and negative periodicity

“…This time is zero for a Poissonian RS and is large for strongly sub-and super-Poissonian structures [12,31,33].…”

“…This stationary stochastic point process can be represented as a collection of mathematical points randomly located on the time axis [4][5][6][7][8]. This process is also called the renewal pulse process [9][10][11][12][13]. The distances between neighboring points (DBNPs) are also called the waiting times, or holding times, or times between successive events.…”

Role of sub- and super-Poisson noise sources in population dynamics

“…The correlated process which describes the starting of a new colony is a renewal process. This kind of process is described by a sequence or recurrent events, whose effect is to reset to zero the system's memory [52][53][54][55][56][57][58]. As a consequence, the interpulse distances or waiting times (WT's) are mutually independent random variables and the waiting time probability density function is the only basic property needed to define the process.…”