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Abstract

The paper deals with nonnegative stochastic processes X(t,ω)(t ≤ 0) not identically zero with stationary and independent increments right-continuous sample functions and fulfilling the initial condition X(0,ω)=0. The main aim is to study the moments of the random functionals $\int_0^∞ f(X(τ,ω))dτ$ for a wide class of functions f. In particular a characterization of deterministic processes in terms of the exponential moments of these functionals is established.