Geodesic
On stochastic approximation processes with infinite variance
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 3, pp. 546-551

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A stochastic approximation algorithm in the presence of noise is considered. The noise is assumed to have the moment of order $p2$, its variance may be infinite. Convergence of stochastic approximation process with probability 1 and in average is proved. 
@article{TVP_1969_14_3_a16,
     author = {T. P. Krasulina},
     title = {On stochastic approximation processes with infinite variance},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {546--551},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_3_a16/}
}
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T. P. Krasulina. On stochastic approximation processes with infinite variance. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 3, pp. 546-551. http://geodesic.mathdoc.fr/item/TVP_1969_14_3_a16/