Stability of stochastic processes defined by integral functionals

K. Urbanik

Studia Mathematica (1992)

  • Volume: 103, Issue: 3, page 225-238
  • 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 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.

How to cite

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Urbanik, K.. "Stability of stochastic processes defined by integral functionals." Studia Mathematica 103.3 (1992): 225-238. <http://eudml.org/doc/215947>.

@article{Urbanik1992,
abstract = {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.},
author = {Urbanik, K.},
journal = {Studia Mathematica},
keywords = {integral functionals; independent increments},
language = {eng},
number = {3},
pages = {225-238},
title = {Stability of stochastic processes defined by integral functionals},
url = {http://eudml.org/doc/215947},
volume = {103},
year = {1992},
}

TY - JOUR
AU - Urbanik, K.
TI - Stability of stochastic processes defined by integral functionals
JO - Studia Mathematica
PY - 1992
VL - 103
IS - 3
SP - 225
EP - 238
AB - 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.
LA - eng
KW - integral functionals; independent increments
UR - http://eudml.org/doc/215947
ER -

References

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  1. [1] C. Berg and G. Forst, Potential Theory on Locally Compact Abelian Groups, Springer, Berlin 1975. Zbl0308.31001
  2. [2] R. Engelking, General Topology, PWN, Warszawa 1977. 
  3. [3] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, New York 1971. Zbl0219.60003
  4. [4] I. I. Gikhman and A. V. Skorokhod, Theory of Random Processes, Vol. II, Nauka, Moscow 1973 (in Russian). Zbl0132.37902
  5. [5] Yu. V. Linnik and I. V. Ostrovskiǐ, Decompositions of Random Variables and Vectors, Nauka, Moscow 1972 (in Russian). 

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