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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