Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction and analysis of sticky reflected diffusions   We give a Dirichlet form approach for the construction of distorted Brownian
motion in a bounded domain $\Omega$ of $\mathbb{R}^d$, $d \geq 1$, with
boundary $\Gamma$, where the behavior at the boundary is sticky. The
construction covers the case of a static boundary behavior as well as the case
of a diffusion on the hypersurface $\Gamma$ (for $d \geq 2)$. More precisely,
we consider the state space $\overline{\Omega}=\Omega \stackrel{.}{\cup}
\Gamma$, the process is a diffusion process inside $\Omega$, the occupation
time of the process on the boundary $\Gamma$ is positive and the process may
diffuse on $\Gamma$ as long as it sticks on the boundary. The problem is
formulated in an $L^2$-setting and the construction is formulated under weak
assumptions on the coefficients and $\Gamma$. In order to analyze the process
we assume a $C^2$-boundary and some weak differentiability conditions. In this
case, we deduce that the process is also a solution to a given SDE for quasi
every starting point in $\overline{\Omega}$ with respect to the underyling
Dirichlet form. Under the addtional condition that $\{ \varrho =0 \}$ is of
capacity zero, we prove ergodicity of the constructed process and consequently,
we verify that the boundary behavior is indeed sticky. Moreover, we show
($\mathcal{L}^p$-)strong Feller properties which allow to characterize the
constructed process even for every starting point in $\overline{\Omega}
\backslash \{ \varrho=0\}$.

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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas