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[333]-343. 500 $aIncludes index. 650 0$aAlgebraic curves 650 0$aCurves 650 0$aGroup schemes 907 $a.b10767083$b23-02-17$c28-06-02 912 $a991000857769707536 945 $aLE013 14-XX HUS11 (1986)$g1$i2013000115078$lle013$o-$pE0.00$q-$rl$s- $t0$u4$v1$w4$x0$y.i10863333$z28-06-02 996 $aElliptic Curves$9354978 997 $aUNISALENTO 998 $ale013$b01-01-94$cm$da $e-$feng$gus $h0$i1 LEADER 04838nam 22007095 450 001 9910300248603321 005 20200704083756.0 010 $a981-10-0272-X 024 7 $a10.1007/978-981-10-0272-4 035 $a(CKB)3710000000541916 035 $a(EBL)4217715 035 $a(SSID)ssj0001597392 035 $a(PQKBManifestationID)16297883 035 $a(PQKBTitleCode)TC0001597392 035 $a(PQKBWorkID)14886282 035 $a(PQKB)10402461 035 $a(DE-He213)978-981-10-0272-4 035 $a(MiAaPQ)EBC4217715 035 $z(PPN)258870583 035 $a(PPN)190884479 035 $a(EXLCZ)993710000000541916 100 $a20151224d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPoisson Point Processes and Their Application to Markov Processes /$fby Kiyosi Itô 205 $a1st ed. 2015. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2015. 215 $a1 online resource (54 p.) 225 1 $aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333 300 $aDescription based upon print version of record. 311 $a981-10-0271-1 320 $aIncludes bibliographical references at the end of each chapters. 327 $aForeword; Preface; References; Contents; 1 Poisson Point Processes; 1.1 Point Functions; 1.2 Point Processes; 1.3 Poisson Point Processes; 1.4 The Structure of Poisson Point Processes (1) the Discrete Case; 1.5 The Structure of Poisson Point Processes (2) the General Case; 1.6 Transformation of Poisson Point Processes; 1.7 Summable Point Processes; 1.8 The Strong Renewal Property of Poisson Point Processes; References; 2 Application to Markov Processes; 2.1 Problem; 2.2 The Poisson Point Process Attached to a Markov Process at a State a; 2.3 The Jumping-In Measure and the Stagnancy Rate 330 $aAn extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ? S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {a} (called the jumping-in measure and a non-negative number m< (called the stagnancy rate). The necessary and sufficient conditions for a pair k, m was obtained so that the correspondence is precisely described. For this, Itô used, as a fundamental tool, the notion of Poisson point processes formed of all excursions of the process on S \ {a}. This theory of Itô's of Poisson point processes of excursions is indeed a breakthrough. It has been expanded and applied to more general extension problems by many succeeding researchers. Thus we may say that this lecture note by Itô is really a memorial work in the extension problems of Markov processes. Especially in Chapter 1 of this note, a general theory of Poisson point processes is given that reminds us of Itô's beautiful and impressive lectures in his day. 410 0$aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333 606 $aProbabilities 606 $aMeasure theory 606 $aFunctional analysis 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aProbabilities. 615 0$aMeasure theory. 615 0$aFunctional analysis. 615 14$aProbability Theory and Stochastic Processes. 615 24$aMeasure and Integration. 615 24$aFunctional Analysis. 676 $a519.23 700 $aItô$b Kiyosi$4aut$4http://id.loc.gov/vocabulary/relators/aut$0344545 702 $aWatanabe$b Shinzo$f1935- 702 $aShigekawa$b Ichiro?$f1953- 712 02$aBernoulli Society for Mathematical Statistics and Probability. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300248603321 996 $aPoisson Point Processes and Their Application to Markov Processes$92498776 997 $aUNINA