This article is cited in 4 papers

Short Communications

On the Solution to the Probability Problem for Non-uniformly Distributed System

A. A. Beilinson

Moscow

Abstract: A dynamical system is considered which is described by a parabolic equation in a circle of length $2l$ when acted upon by an undistributed stochastic force $f(t)$ (white noise)
$$ \frac{\partial W(x,t)}{\partial t}-\frac{\partial^2W(x,t)}{\partial x^2}=\delta(x)f(t). $$
The Green's function for this system (a countable additive measure in the phase space) is constructed. It is proved that almost all $w(x)$ are infinitely differentiable. This measure is not quasi-invariant.

Received: 27.06.1964

 English version: Theory of Probability and its Applications, 1964, 9:3, 469–472

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