Functionals on transient stochastic processes with independent increments

• Autorzy: Kazimierz Urbanik
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60H05: Stochastic integrals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 103
• Numer: 3
• Strony: 299-315

Daty

wydano

1992

otrzymano

1992-05-13

Twórcy

autor

Kazimierz Urbanik

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [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.
• [5] C. M. Goldie, A class of infinitely divisible distributions, Proc. Cambridge Philos. Soc. 63 (1967), 1141-1143.
• [6] M. Loève, Probability Theory, Van Nostrand, New York 1955.
• [7] E. Seneta, Regularly Varying Functions, Lecture Notes in Math. 508, Springer, Berlin 1976.
• [8] A. V. Skorokhod, Random Processes with Independent Increments, Nauka, Moscow 1986 (in Russian).