Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-time ruin probability of aggregate Gaussian processes   Let $\left\{\sum_{i=1}^n \lambda_i X_i(t), t\in [0,T]\right\}$ be an
aggregate Gaussian risk process with $X_i, i\leq n$ independent Gaussian
processes satisfying Piterbarg conditions and $\lambda_i$'s given positive
weights. In this paper we derive exact asymptotics of the finite-time ruin
probability given by $$\mathbb{P}\left(\sup_{t\in[0,T]}\left(\sum_{i=1}^n
\lambda_i X_i(t)- g(t) \right)>u\right)$$ as $u\to\infty$ for some general
trend function $g$. Further, we derive asymptotic results for the finite-time
ruin probabilities of risk processes perturbed by an aggregate Gaussian
process.

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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph