Geodesic
Quenched small deviation for the trajectory of a~random walk with random environment in time
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 2, pp. 322-343

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We consider the small deviation probability for a random walk with random environment in time. Compared to [A. A. Mogul'skii, Theory Probab. Appl., 19 (1975), pp. 726–736], for the independent and identically distributed (i.i.d.) random walk, the rate is smaller (due to the random environment), which is specified in terms of the quenched and annealed variance.
Keywords: random environment, small deviation probability, partial sums of independent random variables. 
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     author = {Y. Lv and W. Hong},
     title = {Quenched small deviation for the trajectory of a~random walk with random environment in time},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {322--343},
     publisher = {mathdoc},
     volume = {68},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2023_68_2_a5/}
}
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Y. Lv; W. Hong. Quenched small deviation for the trajectory of a~random walk with random environment in time. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 2, pp. 322-343. http://geodesic.mathdoc.fr/item/TVP_2023_68_2_a5/