Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the one-sided Tanaka equation with drift   We study questions of existence and uniqueness of weak and strong solutions
for a one-sided Tanaka equation with constant drift \lambda. We observe a
dichotomy in terms of the values of the drift parameter: for \lambda\leq 0,
there exists a strong solution which is pathwise unique, thus also unique in
distribution; whereas for \lambda>0, the equation has a unique in distribution
weak solution, but no strong solution (and not even a weak solution that spends
zero time at the origin). We also show that strength and pathwise uniqueness
are restored to the equation via suitable "Brownian perturbations".

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The categories of this paper are: supr-con
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an