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 タイトル: Determination of the Limiting Coefficient for Exponential Functionals of Random Walks with Positive Drift 著者: Hirano, Katsuhiro 発行日: 1998年 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 5 (1998), No. 2, Page 299-332 抄録: Let $(S_n, n\ge 1)$ be a random walk satisfying $ES_1>0$ and $h$ be a Laplace transform of a non-negative finite measure on $(0, \infty)$. Under additional conditions of $S_1$ and $h$, we consider the asymptotic behavior of $Eh(\sum_{i=1}^ne^{S_i})$. In particular we determine the limiting coefficient for asymptotic of this quantity in terms of the unique solution of the certain functional equation with boundary conditions. This solution corresponds to the Green function of $2^{-1}e^{-x}\triangle$ on {\bf R}. We apply our result to random processes in random media. Moreover we obtain the random walk analogue of Kotani's limit theorem for Brownian motion. URI: http://hdl.handle.net/2261/1345 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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