Moments of some random functionals

• Autorzy: Kazimierz Urbanik
• Języki publikacji: EN

Abstrakty

EN

The paper deals with nonnegative stochastic processes X(t,ω)(t ≤ 0) not identically zero with stationary and independent increments right-continuous sample functions and fulfilling the initial condition X(0,ω)=0. The main aim is to study the moments of the random functionals $\int_0^∞ f(X(τ,ω))dτ$ for a wide class of functions f. In particular a characterization of deterministic processes in terms of the exponential moments of these functionals is established.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1997
• Tom: 74
• Numer: 1
• Strony: 101-108

Daty

wydano

1997

otrzymano

1996-12-03

Twórcy

autor

Kazimierz Urbanik

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

Bibliografia

• [1] C. Berg and G. Forst, Potential Theory on Locally Compact Abelian Groups, Springer, Berlin, 1975.
• [2] I. I. Gikhman and A. V. Skorokhod, Theory of Random Processes, Vol. II, Nauka, Moscow, 1973 (in Russian).
• [3] K. Urbanik, Functionals on transient stochastic processes with independent increments, Studia Math. 103 (1992), 299-315.
• [4] K. Urbanik, Stability of stochastic processes defined by integral functionals, ibid. 103 (1992), 225-238.
• [5] E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, J. London Math. Soc. 10 (1935), 286-293.\vadjust\eject
• [6] E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc. London Math. Soc. 46 (1940), 389-408.