Functionals on transient stochastic processes with independent increments

K. Urbanik

Studia Mathematica (1992)

  • Volume: 103, Issue: 3, page 299-315
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Urbanik, K.. "Functionals on transient stochastic processes with independent increments." Studia Mathematica 103.3 (1992): 299-315. <http://eudml.org/doc/215954>.

@article{Urbanik1992,
abstract = {The paper is devoted to the study of integral functionals $ʃ_0^∞ f(X(t,ω))dt$ 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.},
author = {Urbanik, K.},
journal = {Studia Mathematica},
keywords = {integral functionals; independent increments; random analogue of the Tauberian theorem},
language = {eng},
number = {3},
pages = {299-315},
title = {Functionals on transient stochastic processes with independent increments},
url = {http://eudml.org/doc/215954},
volume = {103},
year = {1992},
}

TY - JOUR
AU - Urbanik, K.
TI - Functionals on transient stochastic processes with independent increments
JO - Studia Mathematica
PY - 1992
VL - 103
IS - 3
SP - 299
EP - 315
AB - The paper is devoted to the study of integral functionals $ʃ_0^∞ f(X(t,ω))dt$ 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.
LA - eng
KW - integral functionals; independent increments; random analogue of the Tauberian theorem
UR - http://eudml.org/doc/215954
ER -

References

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  1. [1] H. Bateman et al., Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York 1953. 
  2. [2] H. Bateman et al., Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York 1953. 
  3. [3] H. Bateman et al., Tables of Integral Transforms, Vol. 1, McGraw-Hill, New York 1954. 
  4. [4] C. Berg and G. Forst, Potential Theory on Locally Compact Abelian Groups, Springer, Berlin 1975. Zbl0308.31001
  5. [5] C. M. Goldie, A class of infinitely divisible distributions, Proc. Cambridge Philos. Soc. 63 (1967), 1141-1143. Zbl0189.51701
  6. [6] M. Loève, Probability Theory, Van Nostrand, New York 1955. 
  7. [7] E. Seneta, Regularly Varying Functions, Lecture Notes in Math. 508, Springer, Berlin 1976. Zbl0324.26002
  8. [8] A. V. Skorokhod, Random Processes with Independent Increments, Nauka, Moscow 1986 (in Russian). 

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