This proceedings volume contains selected contributions which were presented during the 15th Perm Seminar on Stability Problems for Stochastic Models. Articles present a modern approach to a wide range of stability problems of probability theory and mathematical statistics. Topics include characterization problems, domains of attraction, max-semistable laws, queueing theory, robust estimation, stable distributions, self-adjoint densities, stochastic equations, stochastic inequalities and unbiased estimates. This book should be of interest to researchers working in the fields of probability theory, mathematical statistics and queueing theory.