This article is cited in 2 papers

Short Communications

On a probability problem for a one-dimensional heat equation

N. N. Vakhania

Tbilisi

Abstract: The system (2) for random amplitudes $W_i(t)$ (where $f(t)$ is the derivative of a Wiener process) was considered in [1] in connection with the stochastic heat equation (1) and the two following assertions were obtained:
(a) a solution of the system (2) is a random (normal) element in the Hilbert space $l_2$ for every $t>0$;
(b) almost all solutions $\{W_i(t)\}$ are rapidly decreasing sequences for every $t>0$.
In the present note a simple proof of the assertion (a) is given and the assertion (b) is shown to be wrong.

Received: 13.05.1966

 English version: Theory of Probability and its Applications, 1967, 12:4, 666–667

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