Open AccessOn representations of stochastic processes by Radon measures on D(0,1)
Author(s) -
Jolanta Grala-Michalak,
Artur Michalak
Publication year - 2008
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2008.12.03
Subject(s) - radon , banach space , measure (data warehouse) , radon measure , stochastic process , lévy process , space (punctuation) , mathematics , probability measure , process (computing) , stable process , pure mathematics , discrete mathematics , computer science , statistics , locally compact space , physics , data mining , quantum mechanics , operating system
We provide a necessary and sufficient condition for a stochastic process X = {Xt : t ∈ [0, 1]}, taking values in a real Banach space B, for the existence of a probability Radon measure on the space D((0, 1), B) such that the process {et : t ∈ [0, 1]} consisting of evaluationfunctionals is distributed as X. The condition may be easy verified for Levy processes.