Geodesic
Asymptotic properties of the extinction probability for a~Markov multiplication process
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 845-851

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For sequences $\{\tau_i\}$, $\{\gamma_i\}$ of independent positive random variables the following process is constructed: $Y(0)=x$, $dY/dt=-1$ everywhere except points $t_n=\tau_1+\dots+\tau_n$ where $Y(t_n)=\gamma_n Y(t_n-0)=Y(t_n+0)$. Limit theorems are proved concerning the behaviour of the extinction probability $$ f(x)=\mathbf P(\inf\{Y(t),t\ge 0\}0),\qquad x\to\infty. $$ 
@article{TVP_1977_22_4_a15,
     author = {G. \v{S}. Lev},
     title = {Asymptotic properties of the extinction probability for {a~Markov} multiplication process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {845--851},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a15/}
}
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G. Š. Lev. Asymptotic properties of the extinction probability for a~Markov multiplication process. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 845-851. http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a15/