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- W2286574100 abstract "We consider large exceedence probabilities of the perpetuity sequence $$Y_n = B_1 + A_1 B_2 + cdots + (A_1ldots A_{n-1})B_n, $$ where $(A_n,B_n)$ are i.i.d. random variables with values in ${mathbf R} ^+times {mathbf R}$ and the exceedance times are defined as $tau_u = inf{n:; Y_n>u}$. Applying techniques based on analyzing path behavior of $Y_n$ we provide the asymptotics of the sequence $P[tau_u = rho log u]$, $rho >0$, $uto infty $. This improves essentially the results of cite{BCDZ}, where we identified probabilities $P[tau_u in I_u]$, for some large intervals $I_u$ around $k_u$, with lengths growing at least as $loglog u$. Remarkable analogies and differences to random walks cite{Laley} are discussed." @default.
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- W2286574100 date "2015-12-10" @default.
- W2286574100 modified "2023-09-25" @default.
- W2286574100 title "Pointwise estimates for exceedance times of perpetuity sequences" @default.
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