메뉴 건너뛰기




Volumn 193, Issue 7-8, 2002, Pages 1009-1025

Koenigs function and fractional iterates of probability generating functions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0036662045     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM2002v193n07ABEH000667     Document Type: Article
Times cited : (6)

References (21)
  • 1
    • 0003830266 scopus 로고
    • Presses Universitaires de France, Paris
    • G. Valiron, Fonctions analytiques, Presses Universitaires de France, Paris 1954.
    • (1954) Fonctions analytiques
    • Valiron, G.1
  • 2
    • 0001850893 scopus 로고
    • Some mathematical models for branching processes
    • University of California Press, Berkeley
    • T.E. Harris, "Some mathematical models for branching processes", 2nd Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley 1951, pp. 305-328.
    • (1951) 2nd Berkeley Symposium on Mathematical Statistics and Probability , pp. 305-328
    • Harris, T.E.1
  • 3
    • 0004010598 scopus 로고
    • Springer-Verlag, Berlin; Prentice-Hall, Englewood Cliffs, NJ
    • T.E. Harris, The theory of branching processes, Springer-Verlag, Berlin; Prentice-Hall, Englewood Cliffs, NJ 1963.
    • (1963) The theory of branching processes
    • Harris, T.E.1
  • 4
    • 0011297626 scopus 로고
    • Embeddability of discrete time simple branching processes into continuous time processes
    • S. Karlin and J. McGregor, "Embeddability of discrete time simple branching processes into continuous time processes", Trans. Amer. Math. Soc. 132 (1968), 115-136.
    • (1968) Trans. Amer. Math. Soc. , vol.132 , pp. 115-136
    • Karlin, S.1    McGregor, J.2
  • 5
    • 0000964194 scopus 로고
    • Embedding iterates of analytic functions with two fixed points into continuous semigroups
    • S. Karlin and J. McGregor, "Embedding iterates of analytic functions with two fixed points into continuous semigroups", Trans. Amer. Math. Soc. 132 (1968), 137-145.
    • (1968) Trans. Amer. Math. Soc. , vol.132 , pp. 137-145
    • Karlin, S.1    McGregor, J.2
  • 7
    • 0011381035 scopus 로고
    • Fractional iteration of probability generating functions and imbedding discrete branching processes in continuous processes
    • V.V. Goryainov, "Fractional iteration of probability generating functions and imbedding discrete branching processes in continuous processes", Mat. Sb. 184:5 (1993), 55-74; English transl. in Russian Acad. Sci. Sb. Math. 79 (1994).
    • (1993) Mat. Sb. , vol.184 , Issue.5 , pp. 55-74
    • Goryainov, V.V.1
  • 8
    • 85164656232 scopus 로고
    • English transl.
    • V.V. Goryainov, "Fractional iteration of probability generating functions and imbedding discrete branching processes in continuous processes", Mat. Sb. 184:5 (1993), 55-74; English transl. in Russian Acad. Sci. Sb. Math. 79 (1994).
    • (1994) Russian Acad. Sci. Sb. Math. , vol.79
  • 9
    • 0011337783 scopus 로고
    • Semigroups of probability generating functions, and infinitely splittable random variables
    • V.V. Goryainov, "Semigroups of probability generating functions, and infinitely splittable random variables", Theory of Random Processes 1(17) (1995), 2-9.
    • (1995) Theory of Random Processes , vol.1 , Issue.17 , pp. 2-9
    • Goryainov, V.V.1
  • 10
    • 0002175302 scopus 로고
    • Functional equations and the Galton-Watson processes
    • E. Seneta, "Functional equations and the Galton-Watson processes", Adv. in Appl. Probab. 1 (1969), 1-42.
    • (1969) Adv. in Appl. Probab. , vol.1 , pp. 1-42
    • Seneta, E.1
  • 12
    • 0002467171 scopus 로고
    • Recherches sur les intégrales de certaines équations fonctionelles
    • G. Koenigs, "Recherches sur les intégrales de certaines équations fonctionelles", Ann. École Norm. Sup. (3). 1 (1884), 3-41.
    • (1884) Ann. École Norm. Sup. , vol.1 , Issue.3 , pp. 3-41
    • Koenigs, G.1
  • 13
    • 34447604393 scopus 로고
    • Über itierte Funktionen
    • E. Schröder, "Über itierte Funktionen", Math. Ann. 3 (1871), 296-322.
    • (1871) Math. Ann. , vol.3 , pp. 296-322
    • Schröder, E.1
  • 14
    • 0001970577 scopus 로고
    • Fractional iteration near a fixpoint of multiplier 1
    • I.N. Baker, "Fractional iteration near a fixpoint of multiplier 1", J. Austral. Math. Soc. 4 (1964), 143-148.
    • (1964) J. Austral. Math. Soc. , vol.4 , pp. 143-148
    • Baker, I.N.1
  • 15
    • 84968484100 scopus 로고
    • Iteration and the solution of functional equations for functions analytic in the unit disk
    • C.C. Cowen, "Iteration and the solution of functional equations for functions analytic in the unit disk", Trans. Amer. Math. Soc. 265 (1981), 69-95.
    • (1981) Trans. Amer. Math. Soc. , vol.265 , pp. 69-95
    • Cowen, C.C.1
  • 16
    • 0011345767 scopus 로고    scopus 로고
    • One-parameter semigroups of analytic functions and a composition analogue of infinite divisibility
    • Russian
    • V.V. Goryaǐnov, "One-parameter semigroups of analytic functions and a composition analogue of infinite divisibility", Trudy Inst. Prikl. Mat. Mekh. 5 (2000), 44-57. (Russian).
    • (2000) Trudy Inst. Prikl. Mat. Mekh. , vol.5 , pp. 44-57
    • Goryaǐnov, V.V.1
  • 17
    • 0000774649 scopus 로고
    • Sur l'itération des fonctions analytiques
    • A. Denjoy, "Sur l'itération des fonctions analytiques", C. R. Acad. Sci. Paris Sér. A 182 (1926), 255-257.
    • (1926) C. R. Acad. Sci. Paris Sér. A , vol.182 , pp. 255-257
    • Denjoy, A.1
  • 18
    • 0000774650 scopus 로고
    • Sur l'itération des fonctions
    • J. Wolff, "Sur l'itération des fonctions", C. R. Acad. Sci. Paris Sér. A 182 (1926), 42-43, 200-201.
    • (1926) C. R. Acad. Sci. Paris Sér. A , vol.182 , pp. 42-43
    • Wolff, J.1
  • 19
    • 0000108119 scopus 로고
    • On the iteration of analytic functions in a halfplane. II
    • I.N. Baker and Ch. Pommerenke, "On the iteration of analytic functions in a halfplane. II", J. London Math. Soc. (2) 20 (1979), 255-258.
    • (1979) J. London Math. Soc. , vol.20 , Issue.2 , pp. 255-258
    • Baker, I.N.1    Pommerenke, Ch.2
  • 20
    • 0011332865 scopus 로고
    • On asymptotic iteration of analytic functions in the disk
    • Ch. Pommerenke, "On asymptotic iteration of analytic functions in the disk", Analysis (Munich) 1 (1981), 45-61.
    • (1981) Analysis (Munich) , vol.1 , pp. 45-61
    • Pommerenke, Ch.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.