Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete approximations to reflected Brownian motion   In this paper we investigate three discrete or semi-discrete approximation
schemes for reflected Brownian motion on bounded Euclidean domains. For a class
of bounded domains $D$ in $\mathbb{R}^n$ that includes all bounded Lipschitz
domains and the von Koch snowflake domain, we show that the laws of both
discrete and continuous time simple random walks on $D\cap2^{-k}\mathbb{Z}^n$
moving at the rate $2^{-2k}$ with stationary initial distribution converge
weakly in the space $\mathbf{D}([0,1],\mathbb{R}^n)$, equipped with the
Skorokhod topology, to the law of the stationary reflected Brownian motion on
$D$. We further show that the following ``myopic conditioning'' algorithm
generates, in the limit, a reflected Brownian motion on any bounded domain $D$.
For every integer $k\geq1$, let $\{X^k_{j2^{-k}},j=0,1,2,...\}$ be a discrete
time Markov chain with one-step transition probabilities being the same as
those for the Brownian motion in $D$ conditioned not to exit $D$ before time
$2^{-k}$. We prove that the laws of $X^k$ converge to that of the reflected
Brownian motion on $D$. These approximation schemes give not only new ways of
constructing reflected Brownian motion but also implementable algorithms to
simulate reflected Brownian motion.

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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
19
The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex