TY - BOOK ID - 17209536 TI - Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems AU - Gyllenberg, Mats, AU - Silvestrov, Dmitrii S PY - 2008 VL - 44 SN - 09386572 SN - 9783110204377 3110204371 9786613396860 1283396866 3110208253 9783110208252 9781283396868 PB - Berlin Boston DB - UniCat KW - Quasistationarer Zustand KW - Stochastisches System KW - Storungstheorie KW - Stochastic systems. KW - Stochastic processes. KW - Random processes KW - Systems, Stochastic KW - Probabilities KW - Stochastic processes KW - System analysis KW - Markov Chains. KW - Nonlinearly Perturbed Regenerative Processes. KW - Renewal Equation. KW - Semi-Markov Processes. UR - https://www.unicat.be/uniCat?func=search&query=sysid:17209536 AB - The book is devoted to studies of quasi-stationary phenomena in nonlinearly perturbed stochastic systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on new types of asymptotic expansions for perturbed renewal equation and recurrence algorithms for construction of asymptotic expansions for Markov type processes with absorption are presented. Asymptotic expansions are given in mixed ergodic (for processes) and large deviation theorems (for absorption times) for nonlinearly perturbed regenerative processes, semi-Markov processes, and Markov chains. Applications to analysis of quasi-stationary phenomena in nonlinearly perturbed queueing systems, population dynamics and epidemic models, and for risk processes are presented. The book also contains an extended bibliography of works in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications and may be also useful for doctoral and advanced undergraduate students. ER -