On the multiplicity of a~sum of orthogonal processes

T. N. Siraya

Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 4, pp. 880-884

Résumé

Let $x_1(t),\dots,x_n(t)$, $t\in R^1$, be mutually orthogonal stochastic processes of multiplicity 1, $\displaystyle x_0(t)=\sum_1^nx_j(t)$. The problem is to determine the multiplicity of $x_0(t)$. In the note, the following two special cases are considered: 1) the processes $x_1,\dots,x_n$ are spectrally orthogonal, i. e. their closed linear spans satisfy the condition $$ H(x_0,t)=\sum_1^n\oplus H(x_j,t); $$ 2) $n=2$, and $x_1$ and $x_2$ may be either ordinary or generalized stochastic processes.