# Functionals on transient stochastic processes with independent increments

Studia Mathematica (1992)

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

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topUrbanik, 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

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

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