Again on the derivatives of random functions

Caristi, Giuseppe (1999) Again on the derivatives of random functions. Accademia Peloritana dei Pericolanti, Classe di Scienze FF. MM. NN., 76-77. pp. 277-283.

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Abstract

In this paper, two properties are shown to be valid for the derivatives of random functions:
1° Let $X(t,w)$ and $Y(t,w)$ be two random functions, defined in an interval I, which are mean derivables of order $p$ in the point $t_0 \in \ I$ , then:
The sum $X(t,w) + Y(t,w)$ is mean derivable of order $p$ in the point $t_0$ and we have:
$(X+Y)'(t_0,w)=X'(t_0,w)+Y'(t_0,w)$ .
2° Let $X(t,w)$ and $Y(t,w)$ be two indipendent random functions, defined in an interval I, which are mean derivables of order $p$ in the point $t_0 \in \ I$ , then:
The product $X(t,w)\cdot \ Y(t,w)$ is mean derivable of order $p$ in the point $t_0$ and we have:
$(X \cdot \ Y)'(t_0,w)=X'(t_0,w) \cdot \ Y'(t_0,w)$ .
In a preceding paper we have shown two theorems on mean square derivatives of the random functions. In this paper we prove two theorems concerning the mean derivatives of order $p$ of the random functions.

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Item Type:	Article
Subjects:	M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali > 1998-99
Depositing User:	Dr A F
Date Deposited:	18 Sep 2012 07:54
Last Modified:	18 Sep 2012 07:54
URI:	http://cab.unime.it/mus/id/eprint/605

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