04251nam a22005415i 4500 978-3-031-49306-5 DE-He213 20251030112027.0 cr nn 008mamaa 240503s2024 sz | s |||| 0|eng d 9783031493065 978-3-031-49306-5 10.1007/978-3-031-49306-5 doi QA273.A1-274.9 PBT bicssc PBWL bicssc MAT029000 bisacsh PBT thema PBWL thema Brémaud, Pierre. author. aut http://id.loc.gov/vocabulary/relators/aut 76352 An Introduction to Applied Probability [electronic resource] / by Pierre Brémaud. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XIII, 492 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Texts in Applied Mathematics, 2196-9949 ; 77 Preface -- Basic Notions -- Discrete Random Variables -- Continuous Random Vectors -- The Lebesgue Integral -- From Integral to Expectation -- Convergence Almost Sure -- Convergence in Distribution -- Martingales -- Markov Chains -- Poisson Processes -- Brownian Motion -- Wide-sense Stationary Processes -- A Review of Hilbert Spaces -- Bibliography -- Index. This book provides the elements of probability and stochastic processes of direct interest to the applied sciences where probabilistic models play an important role, most notably in the information and communications sciences, computer sciences, operations research, and electrical engineering, but also in fields like epidemiology, biology, ecology, physics, and the earth sciences. The theoretical tools are presented gradually, not deterring the readers with a wall of technicalities before they have the opportunity to understand their relevance in simple situations. In particular, the use of the so-called modern integration theory (the Lebesgue integral) is postponed until the fifth chapter, where it is reviewed in sufficient detail for a rigorous treatment of the topics of interest in the various domains of application listed above. The treatment, while mathematical, maintains a balance between depth and accessibility that is suitable for the efficient manipulation, based on solid theoretical foundations, of the four most important and ubiquitous categories of probabilistic models: Markov chains, which are omnipresent and versatile models in applied probability Poisson processes (on the line and in space), occurring in a range of applications from ecology to queuing and mobile communications networks Brownian motion, which models fluctuations in the stock market and the "white noise" of physics Wide-sense stationary processes, of special importance in signal analysis and design, as well as in the earth sciences. This book can be used as a text in various ways and at different levels of study. Essentially, it provides the material for a two-semester graduate course on probability and stochastic processes in a department of applied mathematics or for students in departments where stochastic models play an essential role. The progressive introduction of concepts and tools, along with the inclusion of numerous examples, also makes this book well-adapted for self-study. Probabilities. 65724 Graph theory. Probability Theory. 67428 Applied Probability. 65727 Graph Theory in Probability. 76353 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031493058 Printed edition: 9783031493072 Texts in Applied Mathematics, 2196-9949 ; 77 76354 https://doi.org/10.1007/978-3-031-49306-5 ZDB-2-SMA ZDB-2-SXMS 59636 59636