Geodesic
Semi-Markov Processes of Multiplication with Drift
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 1, pp. 160-166

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For sequences $\tau_1,\tau_2,\dots$; $\gamma_1,\gamma_2,\dots$ of independent positive random variables the following process is constructed: $Y(0)=x$, $\dfrac{dY}{dt}=-1$ everywhere except at the points $t_k=\sum\limits_{i=1}^k\tau_i$ for which $Y(t_i)=Y(t_i+0)=\gamma_iY(t_i-0)$. Limit theorems are proved concerning the behaviour of $Y(t)$ and $Y(t_n)$ when $t,n\to\infty$. 
@article{TVP_1972_17_1_a14,
     author = {G. Sh. Lev},
     title = {Semi-Markov {Processes} of {Multiplication} with {Drift}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {160--166},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_1_a14/}
}
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G. Sh. Lev. Semi-Markov Processes of Multiplication with Drift. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 1, pp. 160-166. http://geodesic.mathdoc.fr/item/TVP_1972_17_1_a14/