Geodesic
On the distribution of the absorption moment for semimarkov multiplication process
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 4, pp. 880-885

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Let $\{\tau_i\}_{i=1}^{\infty}$ and $\{\gamma_i\}_{i=1}^{\infty}$ be independent sequences of independent positive random variables. For the process $$ Y_n=\gamma_1\gamma_2\dots\gamma_n(x-\xi_n),\quad\text{where}\quad \xi_n=\sum_{i=1}^n\tau_i/\gamma_1\gamma_2\dots\gamma_{i-1}, $$ we consider a random variable $\zeta(x)=\inf\{n\colon Y_n\le 0\ (Y_0=x)\}$ and investigate its limit distributions when $x\to\infty$. 
@article{TVP_1979_24_4_a21,
     author = {G. \v{S}. Lev},
     title = {On the distribution of the absorption moment for semimarkov multiplication process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {880--885},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a21/}
}
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G. Š. Lev. On the distribution of the absorption moment for semimarkov multiplication process. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 4, pp. 880-885. http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a21/