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.

PDF
atti_3_1998-1999_277.pdf - Submitted Version Restricted to users from Unime Download (924kB) | Request a copy |

## 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 |

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 |

### Actions (login required)

View Item |