# Stability of stochastic processes defined by integral functionals

Studia Mathematica (1992)

- Volume: 103, Issue: 3, page 225-238
- ISSN: 0039-3223

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topUrbanik, 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

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

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