Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moments and growth indices for the nonlinear stochastic heat equation
  with rough initial conditions   We study the nonlinear stochastic heat equation in the spatial domain
$\mathbb {R}$, driven by space-time white noise. A central special case is the
parabolic Anderson model. The initial condition is taken to be a measure on
$\mathbb {R}$, such as the Dirac delta function, but this measure may also have
noncompact support and even be nontempered (e.g., with exponentially growing
tails). Existence and uniqueness of a random field solution is proved without
appealing to Gronwall's lemma, by keeping tight control over moments in the
Picard iteration scheme. Upper bounds on all $p$th moments $(p\ge2)$ are
obtained as well as a lower bound on second moments. These bounds become
equalities for the parabolic Anderson model when $p=2$. We determine the growth
indices introduced by Conus and Khoshnevisan [Probab. Theory Related Fields 152
(2012) 681-701].

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The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
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The categories of this paper are: nlin
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph