Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bridges of L\'{e}vy processes conditioned to stay positive   We consider Kallenberg's hypothesis on the characteristic function of a
L\'{e}vy process and show that it allows the construction of weakly continuous
bridges of the L\'{e}vy process conditioned to stay positive. We therefore
provide a notion of normalized excursions L\'{e}vy processes above their
cumulative minimum. Our main contribution is the construction of a continuous
version of the transition density of the L\'{e}vy process conditioned to stay
positive by using the weakly continuous bridges of the L\'{e}vy process itself.
For this, we rely on a method due to Hunt which had only been shown to provide
upper semi-continuous versions. Using the bridges of the conditioned L\'{e}vy
process, the Durrett-Iglehart theorem stating that the Brownian bridge from $0$
to $0$ conditioned to remain above $-\varepsilon$ converges weakly to the
Brownian excursion as $\varepsilon \to0$, is extended to L\'{e}vy processes. We
also extend the Denisov decomposition of Brownian motion to L\'{e}vy processes
and their bridges, as well as Vervaat's classical result stating the
equivalence in law of the Vervaat transform of a Brownian bridge and the
normalized Brownian excursion.

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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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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: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat