Y. Lv, W. Hong, “Quenched small deviation for the trajectory of a random walk with random environment in time”, Teor. Veroyatnost. i Primenen., 2023, Volume 68, Issue 2,Pages <nobr>322

Quenched small deviation for the trajectory of a random walk with random environment in time

Y. Lv^a, W. Hong^b

^a College of Science, Donghua University, Shanghai, China
^b School of Mathematical Sciences and Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, China

Abstract: 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.

MSC: 60G50

Received: 08.10.2021
Revised: 14.06.2022

DOI: 10.4213/tvp5532