Geodesic
Limit theorems for products of independent triangular matrices
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 1, pp. 164-169

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The aim of the present paper is to study the limit distribution for the complete group of triangular matrices with non-negative elements on the diagonal. It is shown, that the distribution of the properly normalized product $G_n$ converges weakly to the distribution of $W^l$, where $W^l$ is the triangular matrix elements of which are some functionals of an $l$-dimensional Wiener process. An explicit form of the probability density is obtained in the case of random matrices $2\times 2$. The probability density of the maximum of some stationary process is also obtained. 
@article{TVP_1977_22_1_a16,
     author = {L. A. Kalenskiǐ},
     title = {Limit theorems for products of independent triangular matrices},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {164--169},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_1_a16/}
}
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L. A. Kalenskiǐ. Limit theorems for products of independent triangular matrices. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 1, pp. 164-169. http://geodesic.mathdoc.fr/item/TVP_1977_22_1_a16/