Messanae Universitas Studiorum

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.

    Item Type: Article
    Subjects: M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali > 1998-99
    Divisions: UNSPECIFIED
    Depositing User: Dr A F
    Date Deposited: 18 Sep 2012 09:54
    Last Modified: 18 Sep 2012 09:54
    URI: http://cab.unime.it/mus/id/eprint/605

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