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Sib. Èlektron. Mat. Izv., 2014, Volume 11, Pages 327–333 (Mi semr490)  

Probability theory and mathematical statistics

Support of diffusion on a cluster Poisson space

O. V. Pugachev

N. E. Bauman Moscow State Technical University

Abstract: We prove that in a space of cluster Poisson configurations on $\mathbb R^d$, under certain conditions, the set of configurations with multiple points has zero $C_{1,2}$ Sobolev capacity. Hence stationary diffusions on this space are supported by the subset of configurations without multiple points.

Keywords: cluster Poisson configurations, capacity, diffusion.

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UDC: 514.132
MSC: 52B15, 51M20, 51M25, 51M09
Received January 28, 2014, published May 14, 2014

Citation: O. V. Pugachev, “Support of diffusion on a cluster Poisson space”, Sib. Èlektron. Mat. Izv., 11 (2014), 327–333

Citation in format AMSBIB
\Bibitem{Pug14}
\by O.~V.~Pugachev
\paper Support of diffusion on a cluster Poisson space
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 327--333
\mathnet{http://mi.mathnet.ru/semr490}


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