LEADER 03605nam 22006375 450 001 9910484004403321 005 20240207160114.0 010 $a3-030-70447-5 024 7 $a10.1007/978-3-030-70447-6 035 $a(CKB)4100000011954524 035 $a(DE-He213)978-3-030-70447-6 035 $a(MiAaPQ)EBC6639218 035 $a(Au-PeEL)EBL6639218 035 $a(OCoLC)1256542336 035 $a(PPN)258062932 035 $a(EXLCZ)994100000011954524 100 $a20210609d2021 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMarkov Renewal and Piecewise Deterministic Processes /$fby Christiane Cocozza-Thivent 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (XIV, 252 p. 16 illus., 4 illus. in color.) 225 1 $aProbability Theory and Stochastic Modelling,$x2199-3149 ;$v100 311 $a3-030-70446-7 320 $aIncludes bibliographical references and index. 327 $aTools -- Markov renewal processes and related processes -- First steps with PDMP -- Hitting time distribution -- Intensity of some marked point pocesses -- Generalized Kolmogorov equations -- A martingale approach -- Stability -- Numerical methods -- Switching Processes -- Tools -- Interarrival distribution with several Dirac measures -- Algorithm convergence's proof. 330 $aThis book is aimed at researchers, graduate students and engineers who would like to be initiated to Piecewise Deterministic Markov Processes (PDMPs). A PDMP models a deterministic mechanism modified by jumps that occur at random times. The fields of applications are numerous : insurance and risk, biology, communication networks, dependability, supply management, etc. Indeed, the PDMPs studied so far are in fact deterministic functions of CSMPs (Completed Semi-Markov Processes), i.e. semi-Markov processes completed to become Markov processes. This remark leads to considerably broaden the definition of PDMPs and allows their properties to be deduced from those of CSMPs, which are easier to grasp. Stability is studied within a very general framework. In the other chapters, the results become more accurate as the assumptions become more precise. Generalized Chapman-Kolmogorov equations lead to numerical schemes. The last chapter is an opening on processes for which the deterministic flow of the PDMP is replaced with a Markov process. Marked point processes play a key role throughout this book. 410 0$aProbability Theory and Stochastic Modelling,$x2199-3149 ;$v100 606 $aMarkov processes 606 $aComputer science$xMathematics 606 $aMathematical statistics 606 $aMarkov Process 606 $aProbability and Statistics in Computer Science 606 $aProcessos de Markov$2thub 606 $aEstadística matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aMarkov processes. 615 0$aComputer science$xMathematics. 615 0$aMathematical statistics. 615 14$aMarkov Process. 615 24$aProbability and Statistics in Computer Science. 615 7$aProcessos de Markov 615 7$aEstadística matemàtica 676 $a519.233 700 $aCocozza-Thivent$b Christiane$0846871 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484004403321 996 $aMarkov Renewal and Piecewise Deterministic Processes$91891974 997 $aUNINA