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We study the rate of convergence of the distribution of the normalized sojourn time of a classical random walk above some nonnegative level to its limit law with unboundedly growing observation time. [ABSTRACT FROM AUTHOR]

We study the asymptotic behavior of the mean sojourn time for a random walk above a receding curved boundary in the case where the jump distribution satisfies the Cramèr condition. [ABSTRACT FROM AUTHOR]

We derive convenient formulas for the tail probabilities of the supnorm of the simplest nonsymmetric random walks defined on a finite time-interval. Using these formulas, we obtain a new representation for the distribution of the number of crossings of a canonical strip by the random walks. As a consequence of the above-mentioned results, we propose a new approach to calculation of the distributions of some boundary functionals of a Wiener process with drift. [ABSTRACT FROM AUTHOR]

We compute the distribution of the number of crossings of a canonical strip by paths of a homogeneous random walk with a three-point distribution of the jump, defined on a finite or an infinite time-interval. By the Donsker-Prokhorov invariance principle (for an array of the random walks), we derive a similar formula for a Wiener process with drift from the above-mentioned result. [ABSTRACT FROM AUTHOR]

For a random walk, we prove a continuity theorem for the exit time from a strip containing the abscissa axis, including the case of the exit time from a strip through an a priori chosen boundary. In particular, we compute the ruin probabilities for two classes of centered distributions. [ABSTRACT FROM AUTHOR]

This paper is essentially an improved result from [V. I. Lotov and N. G. Orlova, Sb. Math., 194 (2003), pp. 927-939], where a formula was obtained for the distribution of the number of crossings of a strip by paths of a random walk defined by an infinite sequence of the partial sums of independent random variables having a common "two-sided geometric" distribution. [ABSTRACT FROM AUTHOR]

Information on the Fifth International Conference titled Limit Theorems in Probability Theory and Their Applications, which was held at the Sobolev Institute of Mathematics in Novosibirsk, Russia from August 15-18, 2011 is presented. Topics include central limit theorem, random walks, and stochastic integrals. The conference featured several speakers including mathematicians A. A. Borovkov and T. Mikosh, and author I. A. Ibragimov.