# Moments of some random functionals

Colloquium Mathematicum (1997)

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

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topUrbanik, 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

top- [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.
- [6] E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc. London Math. Soc. 46 (1940), 389-408.

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