Geodesic
On the Solution to the Probability Problem for Non-uniformly Distributed System
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 3, pp. 519-523

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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. 
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     author = {A. A. Beilinson},
     title = {On the {Solution} to the {Probability} {Problem} for {Non-uniformly} {Distributed} {System}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {519--523},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {1964},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_3_a7/}
}
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A. A. Beilinson. On the Solution to the Probability Problem for Non-uniformly Distributed System. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 3, pp. 519-523. http://geodesic.mathdoc.fr/item/TVP_1964_9_3_a7/