02993nam a22004455i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118040002500153050001900178050001600197072001600213072002300229072001500252072001600267082001400283100008000297245011700377264007500494300006500569336002600634337002600660338003600686347002400722490005300746505028300799520096601082650003802048650012002086650011602206710003402322773002002356776003602376776003602412830005302448856004602501978-3-319-67059-1DE-He21320181204134424.0cr nn 008mamaa171014s2017 gw | s |||| 0|eng d a97833196705917 a10.1007/978-3-319-67059-12doi aISI Library, Kolkata 4aQA273.A1-274.9 4aQA274-274.9 7aPBT2bicssc 7aMAT0290002bisacsh 7aPBT2thema 7aPBWL2thema04a519.22231 aZacks, Shelemyahu.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aSample Path Analysis and Distributions of Boundary Crossing Timesh[electronic resource] /cby Shelemyahu Zacks. 1aCham :bSpringer International Publishing :bImprint: Springer,c2017. aXIII, 135 p. 19 illus., 2 illus. in color.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aLecture Notes in Mathematics,x0075-8434 ;v22030 aIntroduction -- Technical Prerequisites -- First Crossing by Poisson Processes -- First Crossing by Compound Poisson Processes -- Telegraph Processes -- Sequential Estimation -- First Crossing a Random Process -- Failure Times of Deterioration Processes -- Miscellaneous Topics. aThis monograph is focused on the derivations of exact distributions of first boundary crossing times of Poisson processes, compound Poisson processes, and more general renewal processes. The content is limited to the distributions of first boundary crossing times and their applications to various stochastic models. This book provides the theory and techniques for exact computations of distributions and moments of level crossing times. In addition, these techniques could replace simulations in many cases, thus providing more insight about the phenomenona studied. This book takes a general approach for studying telegraph processes and is based on nearly thirty published papers by the author and collaborators over the past twenty five years. No prior knowledge of advanced probability is required, making the book widely available to students and researchers in applied probability, operations research, applied physics, and applied mathematics. . 0aDistribution (Probability theory.14aProbability Theory and Stochastic Processes.0http://scigraph.springernature.com/things/product-market-codes/M2700424aOperations Research, Management Science.0http://scigraph.springernature.com/things/product-market-codes/M260242 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978331967058408iPrinted edition:z9783319670607 0aLecture Notes in Mathematics,x0075-8434 ;v220340uhttps://doi.org/10.1007/978-3-319-67059-1