Determining the Distribution of Values of Stochastic Impulses Acting on a Discrete System in Relation to Their Intensity

Abstract

In our previous works we introduced and applied a mathematical model that allowed us to calculate the approximate distribution of the values of stochastic impulses i forcing vibrations of an oscillator with damping from the trajectory of its movement. The mathematical model describes correctly the functioning of a physical RLC system if the coecient of damping is large and the intensity of impulses is small. It is so because the inow of energy is small and behaviour of RLC is stable. In this paper we are going to present some experiments which characterize the behaviour of an oscillator RLC in relation to the intensity parameter , precisely to E(). The parameter is a constant in the exponential distribution of random variables i, where i = ti -ti-1, i = 1, 2, . . . are intervals between successive impulses.