This book explores various advanced topics in probability theory and stochastic processes. It begins with stability problems in multi-channel queueing systems and networks, followed by analogues of the Berry-Esseen estimate for associated random fields. The text delves into exact-order estimates of decomposition stability within the Levy metric for convolutions of Gaussian and Poisson laws. It also addresses convergence in law for sums of independent Banach-valued random elements with random coefficients and examines stochastic processes alongside harmonic analysis on Gel'fand pairs. Further discussions include max-semistable laws under linear and power normalization, unbiased estimators for density functions and probabilities of linear inequalities in the multivariate normal case, and the domain of normal attraction of stable distributions on the semidirect product of a compact group and \( \mathbb{R}^d \). The stability of the inverse Radon transformation and mathematical methods for reliability growth analysis are also covered. The book presents uniform stability of semi-Markov process distributions, the strong law of large numbers, and relationships between densities of strictly stable measures. It investigates the convergence of pointwise maxima of specific random functions, high deviations for multidimensional stationary Gaussian processes, and central limit theorems based on conditional moments. Additional topics incl
