Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liouville distorted Brownian motion   The Liouville Brownian motion was introduced in \cite{GRV} as a time changed
process $B_{A_t^{-1}}$ of a planar Brownian motion $(B_t)_{t \ge 0}$, where
$(A_t)_{t \ge 0}$ is the positive continuous additive functional of $(B_t)_{t
\ge 0}$ in the strict sense w.r.t. the Liouville measure. We first consider a
distorted Brownian motion $(X_t)_{t\ge0}$ starting from all points in $\R^2$
associated to a Dirichlet form $(\E, D(\E))$ (see \cite{ShTr14}). We show that
the positive continuous additive functional $(F_t)_{t \ge 0}$ of $(X_t)_{t \ge
0}$ in the strict sense w.r.t. the Liouville distorted measure can be
constructed.

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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio