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020 _a9783031493065
_9978-3-031-49306-5
024 7 _a10.1007/978-3-031-49306-5
_2doi
050 4 _aQA273.A1-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
100 1 _aBrémaud, Pierre.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_976352
245 1 3 _aAn Introduction to Applied Probability
_h[electronic resource] /
_cby Pierre Brémaud.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXIII, 492 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTexts in Applied Mathematics,
_x2196-9949 ;
_v77
505 0 _aPreface -- 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.
520 _aThis 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.
650 0 _aProbabilities.
_965724
650 0 _aGraph theory.
650 1 4 _aProbability Theory.
_967428
650 2 4 _aApplied Probability.
_965727
650 2 4 _aGraph Theory in Probability.
_976353
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031493058
776 0 8 _iPrinted edition:
_z9783031493072
830 0 _aTexts in Applied Mathematics,
_x2196-9949 ;
_v77
_976354
856 4 0 _uhttps://doi.org/10.1007/978-3-031-49306-5
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c59636
_d59636