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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1965, Volume 10, Issue 4, Pages 736–741 (Mi tvp586)

Short Communications

On the evolution of distributed systems when there is a fluctuation of the density on the boundary

A. A. Beilinson

Moscow

Abstract: A dynamical system is considered which is described by a parabolic equation in a circle of length $2\pi$ when acted upon by an undistributed stochastic source with a power $\dot\pi(t)$ (the derivative of Poisson's process):
$$\frac{\partial W(x,t)}{\partial t}-D^2\frac{\partial^2W(x,t)}{\partial x^2}=\delta(x)\dot\pi(t).$$
The characteristic functional for this system which defines a countable additive measure iii the phase space is constructed. It is proved that almost all $W(x)$ are infinitely differentiable. This measure is not quasi-invariant.

Full text: PDF file (409 kB)

English version:
Theory of Probability and its Applications, 1965, 10:4, 668–673

Bibliographic databases:

Citation: A. A. Beilinson, “On the evolution of distributed systems when there is a fluctuation of the density on the boundary”, Teor. Veroyatnost. i Primenen., 10:4 (1965), 736–741; Theory Probab. Appl., 10:4 (1965), 668–673

Citation in format AMSBIB
\Bibitem{Bei65} \by A.~A.~Beilinson \paper On the evolution of distributed systems when there is a~fluctuation of the density on the boundary \jour Teor. Veroyatnost. i Primenen. \yr 1965 \vol 10 \issue 4 \pages 736--741 \mathnet{http://mi.mathnet.ru/tvp586} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=189153} \zmath{https://zbmath.org/?q=an:0178.52602} \transl \jour Theory Probab. Appl. \yr 1965 \vol 10 \issue 4 \pages 668--673 \crossref{https://doi.org/10.1137/1110082}