Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sinai's condition for real valued L\'{e}vy processes   We prove that the upward ladder height subordinator $H$ associated to a real
valued L\'{e}vy process $\xi$ has Laplace exponent $\phi$ that varies regularly
at $\infty$ (resp. at 0) if and only if the underlying L\'{e}vy process $\xi$
satisfies Sinai's condition at 0 (resp. at $\infty$). Sinai's condition for
real valued L\'{e}vy processes is the continuous time analogue of Sinai's
condition for random walks. We provide several criteria in terms of the
characteristics of $\xi$ to determine whether or not it satisfies Sinai's
condition. Some of these criteria are deduced from tail estimates of the
L\'{e}vy measure of $H,$ here obtained, and which are analogous to the
estimates of the tail distribution of the ladder height random variable of a
random walk which are due to Veraverbeke and Gr\"{u}bel

18
The categories of this paper are: econ
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg