In previous papers formulas have been derived describing distribution of a random variable whose values are positions of an oscillator at the moment t, which, in the interval [0, t], underwent the influence of stochastic impulses with a given distribution. In this paper we present reasoning leading to an opposite inference thanks to which, knowing the course of the oscillator, we can find the approximation of distribution of stochastic impulses acting on it. It turns out that in the case of an oscillator with damping the stochastic process ξ t of its deviations at the moment t is a stationary and ergodic process for large t. Thanks to this, time average of almost every trajectory of the process, which is the n-th power of ξ t is very close to the mean value of ξ n t in space for sufficiently large t. Thus, having a course of a real oscillator and theoretical formulae for the characteristic function ξ t we are able to calculate the approximate distribution of stochastic impulses forcing the oscillator.

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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 ηi 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 λ 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 λ, precisely to λE(η). The parameter λ is a constant in the exponential distribution of random variables τi, where τi = ti − ti−1, i = 1, 2, . . . are intervals between successive impulses.

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It is shown that for any z ~z 0 and for any integrable function /: [0,1]-» R+ the measure \í¡ (where ¡i is Lebesgue measure and \í¡ is defined by dfi¡ = fd\i) of the set of points x for which |f(x) < z/e tends to an exponential function of z as e tends to zero.