Moments of some random functionals

K. Urbanik

Colloquium Mathematicum (1997)

  • Volume: 74, Issue: 1, page 101-108
  • ISSN: 0010-1354

Abstract

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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 ∫ 0 ∞ f ( X ( τ , ω ) ) d τ 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.

How to cite

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Urbanik, K.. "Moments of some random functionals." Colloquium Mathematicum 74.1 (1997): 101-108. <http://eudml.org/doc/210493>.

@article{Urbanik1997,
abstract = {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.},
author = {Urbanik, K.},
journal = {Colloquium Mathematicum},
keywords = {nonnegative stochastic processes; stationary and independent increments; random functionals; exponential moments},
language = {eng},
number = {1},
pages = {101-108},
title = {Moments of some random functionals},
url = {http://eudml.org/doc/210493},
volume = {74},
year = {1997},
}

TY - JOUR
AU - Urbanik, K.
TI - Moments of some random functionals
JO - Colloquium Mathematicum
PY - 1997
VL - 74
IS - 1
SP - 101
EP - 108
AB - 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.
LA - eng
KW - nonnegative stochastic processes; stationary and independent increments; random functionals; exponential moments
UR - http://eudml.org/doc/210493
ER -

References

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

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