Moments of some random functionals
Tom 74 / 1997
Colloquium Mathematicum 74 (1997), 101-108
DOI: 10.4064/cm-74-1-101-108
Streszczenie
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.
