On the Feller strong law of large numbers for fields of -valued random variables.
Lagodowski, Zbigniew A. (1994)
Mathematica Pannonica
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Displaying similar documents to “Renewal theory in dimensions (I)”
On the Feller strong law of large numbers for fields of -valued random variables.
Problem of uniqueness in the renewal process generated by the uniform distribution.
Ugrin-Šparac, D. (1992)
Journal of Applied Mathematics and Stochastic Analysis
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On the moments of sums of independent identically distributed random variables.
Túri, József (2006)
Mathematica Pannonica
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On shifting iterated convolutions II
A. J. Stam (1967)
Compositio Mathematica
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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 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.
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 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 with a ∈ (0,∞) is discussed.
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...
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...