This book covers a range of topics in probability theory and stochastic processes, focusing on multiple-server queues, branching Brownian motion, and various mathematical techniques. It begins with discussions on renovation and regeneration in queues and explores functionals of branching processes. The convergence rates for transient phenomena in these processes are examined, alongside the Wick product and modeling VARMAX processes through advanced statistical methods. The text delves into homogeneous Gaussian diffusions, first passage problems in branching Brownian motions, and the properties of random graphs with marked cycles. It also presents a local limit theorem related to Markov chains converging to diffusion processes and addresses stationary modifications of the log-likelihood function in continuous time system identification. Additionally, it explores the convergence of filtered experiments generated by semimartingales and employs a martingale approach to stochastic approximation procedures. The book discusses a general class of stochastic approximation algorithms and their application in maximum likelihood inference for Markov random fields. Further, it includes topics such as the Edgeworth expansion, convergence rates in the central limit theorem, asymptotic properties of maximum likelihood estimators, and the dynamics of infinite systems of dissimilar particles. The book concludes with insights into sequential
