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- W1574356718 abstract "Consider an $(L,alpha )$-superdiffusion $X$ on ${mathbb {R}}^{d}$, where $L$ is an uniformly elliptic differential operator in ${mathbb {R}}^{d}$, and $1<alpha le 2$. The $mathbb {G}$-polar sets for $X$ are subsets of $mathbb {R}times {mathbb {R}}^{d}$ which have no intersection with the graph $mathbb {G}$ of $X$, and they are related to the removable singularities for a corresponding nonlinear parabolic partial differential equation. Dynkin characterized the $mathbb {G}$-polarity of a general analytic set $Asubset mathbb {R}times {mathbb {R}}^{d}$ in term of the Bessel capacity of $A$, and Sheu in term of the restricted Hausdorff dimension. In this paper we study in particular the $mathbb {G}$-polarity of sets of the form $Etimes F$, where $E$ and $F$ are two Borel subsets of $mathbb {R}$ and ${mathbb {R}}^{d}$ respectively. We establish a relationship between the restricted Hausdorff dimension of $Etimes F$ and the usual Hausdorff dimensions of $E$ and $F$. As an application, we obtain a criterion for $mathbb {G}$-polarity of $Etimes F$ in terms of the Hausdorff dimensions of $E$ and $F$, which also gives an answer to a problem proposed by Dynkin in the 1991 Wald Memorial Lectures." @default.
- W1574356718 created "2016-06-24" @default.
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- W1574356718 date "1999-05-17" @default.
- W1574356718 modified "2023-09-27" @default.
- W1574356718 title "On a problem of Dynkin" @default.
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- W1574356718 doi "https://doi.org/10.1090/s0002-9939-99-04981-3" @default.
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