Lugavov, V. S. On factorization components of the sojourn times for semicontinuous random walks in a strip. (Russian, English) Zbl 1032.60042 Sib. Mat. Zh. 44, No. 4, 800-809 (2003); translation in Sib. Math. J. 44, No. 4, 629-637 (2003). Let \(\xi_1,\xi_2,\dots\) be independent identically distributed random variables and let \(S_n=\xi_1+\cdots+\xi_n\). Given an interval \((\gamma_1,\gamma_2]\) of the real axis, let \[ u((\gamma_1,\gamma_2],n) =\text{Card}\{k\in[1,n]:S_k\in(\gamma_1,\gamma_2]\} \] be the sojourn time of the random walk \(S_n\) in the interval \((\gamma_1,\gamma_2]\). The special case of so-called semicontinuous random walk is considered when \(\xi\)’s take their values in integers not greater than \(1\). For a random walk of this type, the author obtains explicit representations for factorization components for the distribution of the functional \(u((\gamma_1,\gamma_2],n)\). Reviewer: D.A.Korshunov (Novosibirsk) Cited in 3 Documents MSC: 60G50 Sums of independent random variables; random walks 62E10 Characterization and structure theory of statistical distributions Keywords:sojourn time of a random walk; matrix factorization; Banach algebra PDFBibTeX XMLCite \textit{V. S. Lugavov}, Sib. Mat. Zh. 44, No. 4, 800--809 (2003; Zbl 1032.60042); translation in Sib. Math. J. 44, No. 4, 629--637 (2003) Full Text: EuDML EMIS