Abstract
We consider the problem of the distribution of the sojourn time in a compact set \(\mathbb{Z}_{p}\) in the case of a \(p\)-adic random walk. We rely on the results of our previous studies of the distribution of the first return time for a \(p\)-adic random walk and the results of Takacs on the study of the sojourn time problem for a wide class of random processes. For a \(p\)-adic random walk we find the mean sojourn time of the trajectory in \(\mathbb{Z}_{p}\) and the asymptotics as \(t\rightarrow\infty\) of arbitrary moments of the distribution of the sojourn time in \(\mathbb{Z}_{p}\). We also discuss some possible applications of our results to the modeling of relaxation processes related to the conformational dynamics of protein.
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The study was supported in part by the Ministry of Education and Science of Russia by State assignment to educational and research institutions under project FSSS-2020-0014.
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Bikulov, A.K., Zubarev, A.P. The Sojourn Time Problem for a \(p\)-Adic Random Walk and its Applications. P-Adic Num Ultrametr Anal Appl 14, 265–278 (2022). https://doi.org/10.1134/S207004662204001X
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DOI: https://doi.org/10.1134/S207004662204001X