Displaying similar documents to “Local characteristics of generalized stochastic processes”

Moments of some random functionals

K. Urbanik (1997)

Colloquium Mathematicum

Similarity:

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 0 f ( X ( τ , ω ) ) d τ 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.