Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The first passage time density of Brownian motion and the heat equation
  with Dirichlet boundary condition in time dependent domains   In [4], it is proved that we can have a continuous first-passage-time density
function of one dimensional standard Brownian motion when the boundary is
H\"older continuous with exponent greater than 1/2. For the purpose of
extending [4] into multidimensional domains, we show that there exists a
continuous first-passage-time density function of standard $d$-dimensional
Brownian motion in moving boundaries in $\mathbb{R}^{d}$, $d\geq 2$, under a
$C^{3}$-diffeomorphism. Similarly as in [4], by using a property of local time
of standard $d$-dimensional Brownian motion and the heat equation with
Dirichlet boundary condition, we find a sufficient condition for the existence
of the continuous density function.

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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
14
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: acc-phys
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
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The categories of this paper are: eess