Stability of stochastic processes defined by integral functionals

The paper is devoted to the study of integral functionals ${\displaystyle {ʃ}_0^{\infty }f\left(X(t,\omega )\right)dt}$ for continuous nonincreasing functions f and nonnegative stochastic processes X(t,ω) with stationary and independent increments. In particular, a concept of stability defined in terms of the functionals ${\displaystyle {ʃ}_0^{\infty }f\left(aX(t,\omega )\right)dt}$ with a ∈ (0,∞) is discussed.