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- W2784248780 abstract "In this paper we study the probability $xi_n(u):={mathbb P}left(C_ngeqslant u n right)$, with $C_n:=A(psi_n B(varphi_n))$ for L'evy processes $A(cdot)$ and $B(cdot)$, and $varphi_n$ and $psi_n$ non-negative sequences such that $varphi_n psi_n =n$ and $varphi_ntoinfty$ as $ntoinfty$. Two timescale regimes are distinguished: a 'fast' regime in which $varphi_n$ is superlinear and a 'slow' regime in which $varphi_n$ is sublinear. We provide the exact asymptotics of $xi_n(u)$ (as $ntoinfty$) for both regimes, relying on change-of-measure arguments in combination with Edgeworth-type estimates. The asymptotics have an unconventional form: the exponent contains the commonly observed linear term, but may also contain sublinear terms (the number of which depends on the precise form of $varphi_n$ and $psi_n$). To showcase the power of our results we include two examples, covering both the case where $C_n$ is lattice and non-lattice." @default.
- W2784248780 created "2018-01-26" @default.
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- W2784248780 date "2018-01-09" @default.
- W2784248780 modified "2023-09-27" @default.
- W2784248780 title "Exact asymptotics for a multi-timescale model" @default.
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