Stability of stochastic processes defined by integral functionals
Volume 103 / 1992
Studia Mathematica 103 (1992), 225-238 DOI: 10.4064/sm-103-3-225-238
The paper is devoted to the study of integral functionals $ʃ_0^∞ f(X(t,ω)) dt$ 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 $ʃ_0^∞ f(aX(t,ω))dt$ with a ∈ (0,∞) is discussed.