Displaying similar documents to “On the moments of sums of independent identically distributed random variables.”

Stability of stochastic processes defined by integral functionals

K. Urbanik (1992)

Studia Mathematica

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The paper is devoted to the study of integral functionals ʃ 0 ∞ f ( X ( t , ω ) ) d t 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 ( a X ( t , ω ) ) d t with a ∈ (0,∞) is discussed.

Functionals on transient stochastic processes with independent increments

K. Urbanik (1992)

Studia Mathematica

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The paper is devoted to the study of integral functionals ʃ 0 ∞ f ( X ( t , ω ) ) d t for a wide class of functions f and transient stochastic processes X(t,ω) with stationary and independent increments. In particular, for nonnegative processes a random analogue of the Tauberian theorem is obtained.

Infinitely divisible processes and their potential theory. II

Sidney C. Port, Charles J. Stone (1971)

Annales de l'institut Fourier

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This second part of our two part work on i.d. process has four main goals: (1) To develop a potential operator for recurrent i.d. (infinitely divisible) processes and to use this operator to find the asymptotic behavior of the hitting distribution and Green’s function for relatively compact sets in the recurrent case. (2) To develop the appropriate notion of an equilibrium measure and Robin’s constant for Borel sets. (3) To establish the asymptotic...