Miary losowe

• Autorzy: Stanisław Krowicki , Wojciech Rybicki

Warianty tytułu

Random Measures

• Języki publikacji: PL

Abstrakty

Opisano funkcyjne i miarowe podejście do zagadnienia miar stochastycznych. Przedstawiono miary losowe i procesy punktowe oraz miary całkowicie losowe i rozkłady nieskończenie podzielne.

EN

The purpose of this paper is to investigate an idea of random measures. We start with polemics with extremely oriented researchers on absurdity of some controversioes focused on meaning (and correctness) of terms and verbs. They seem especially unreasonable when confronted with reasonable serious science - the cases of "mechanistic" apologizing versus total removing of notions like "probability", "random", are the best examples to illustrate the subject.
The title of section 1 - "Functional and measure-theoretical approaches to the problem of stochastic measures" - completely reflects its content. Roughly speaking: random measure can be considered as a measurable mapping from some probability space into the space of measures on a fixed n-algebra of subsets of some set. The essence of the second approach is defining a random measure as a set function taking values in some class of random variables. We discuss the relations between various treatments of random measures.
In the third, final section, we report some facts concerning random measures - which generalize the notion of stochastic processes with independent increments. The theory of infinite divisibility have to appear in this context. (original abstract)

Słowa kluczowe

PL

Modele stochastyczne; Analiza procesów losowych

EN

Stochastic models; Analysis of random processes

• Czasopismo: Prace Naukowe Akademii Ekonomicznej we Wrocławiu
• Rocznik: 1995
• Numer: nr 696 Dydaktyka matematyki
• Strony: 45--54

Twórcy

autor

Stanisław Krowicki

autor

Wojciech Rybicki

Bibliografia

• Billingsley P.: Convergence of probability measures. New York: J. Wiley and Sons 1968.
• Feller W.: Wstęp do rachunku prawdopodobieństwa. Warszawa: PWN 1968.
• Gichman I.I., Skorochod A.W.: Wstęp do teorii procesów stochastycznych. Warszawa: PWN 1968.
• Grandell J.: Doubly Stochastic Poisson Processes. Berlin-Heidelberg-New York: Springer-Verlag 1976.
• Kallenberg О.: Random Measures. London-New York-San Francisco: Academic Press and Berlin: Akademik Verlag 1976.
• Kingman J.F.G.: Completely Random Measures. "Pacific Journal of Mathematics" 21 (1967), s. 59-78.
• Prekopa A.: On stochastic set functions I. (1956). "Acta Math. Acad. Sci. Hungar." vol. 7, s. 215-267.
• Rybicki W.: Miary wektorowe. "Prace Naukowe AE we Wrocławiu" (1995). "Dydaktyka Matematyki" (w niniejszym zeszycie).
• Urbanik K.: Some prediction problems for stricly stationary processes "Proceedings of the Fifth Berkeley Symp. on Math. Statistics and Probability" (1965).