On the Number of Solutions of Systems of Random Equations

Brillinger, David R.

Ann. Math. Statist., Tome 43 (1972) no. 6, p. 534-540 / Harvested from Project Euclid

Résumé

Let $\{f(x, \omega); x \in R^n, \omega \in \Omega \}$ be an $n$ vector-valued stochastic process defined over a probability space $(\Omega, \mathscr{A}, \mu)$. Let $N(f \mid A, y)$ denote the number of elements in the set $A \cap f^{-1}(y)$, that is the number of distinct solutions of the system of equations $f(x, \omega) = y$ for $x, y \in R^n$. We develop expressions for $E\{N(f \mid A, y)\}$ and certain higher-order moments of $N(f \mid A, y)$ under regularity conditions.

Publié le : 1972-04-14
Classification:

@article{1177692634,
     author = {Brillinger, David R.},
     title = {On the Number of Solutions of Systems of Random Equations},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 534-540},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692634}
}

Brillinger, David R. On the Number of Solutions of Systems of Random Equations. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  534-540. http://gdmltest.u-ga.fr/item/1177692634/