Displaying similar documents to “Stability of stochastic processes defined by integral functionals”

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...

A characterization of probability measures by f-moments

K. Urbanik (1996)

Studia Mathematica

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Given a real-valued continuous function ƒ on the half-line [0,∞) we denote by P*(ƒ) the set of all probability measures μ on [0,∞) with finite ƒ-moments ʃ 0 ∞ ƒ ( x ) μ * n ( d x ) (n = 1,2...). A function ƒ is said to have the identification propertyif probability measures from P*(ƒ) are uniquely determined by their ƒ-moments. A function ƒ is said to be a Bernstein function if it is infinitely differentiable on the open half-line (0,∞) and ( - 1 ) n ƒ ( n + 1 ) ( x ) is completely monotone for some nonnegative integer n. The purpose...

Infinitely divisible processes and their potential theory. I

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

Annales de l'institut Fourier

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We show that associated with every i.d. (infinitely divisible) process on a locally compact, non-compact 2nd countable Abelian group is a corresponding potential theory that yields definitive results on the behavior of the process in both space and time. Our results are general, no density or other smoothness assumptions are made on the process. In this first part of two part work we have four main goals. (1) To lay the probabilistic foundation of such processes. This mainly...

Moments of some random functionals

K. Urbanik (1997)

Colloquium Mathematicum

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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.