Geodesic
Moments of some random functionals
Colloquium Mathematicum, Tome 74 (1997) no. 1, pp. 101-108

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DOI

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. 
K. Urbanik. Moments of some random functionals. Colloquium Mathematicum, Tome 74 (1997) no. 1, pp. 101-108. doi: 10.4064/cm-74-1-101-108
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