메뉴 건너뛰기




Volumn 28, Issue 3, 1996, Pages 853-876

First crossing of basic counting processes with lower non-linear boundaries: A unified approach through pseudopolynomials (I)

Author keywords

Abel Gontcharoff polynomials; Appell polynomials; Lower and upper boundaries

Indexed keywords


EID: 0000827499     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800046528     Document Type: Article
Times cited : (35)

References (25)
  • 1
    • 3142529598 scopus 로고
    • Sur les fonctions génératrices et leurs déterminantes
    • ABEL, N. (1881) Sur les fonctions génératrices et leurs déterminantes. Oeuvres Complètes. Vol 2. pp. 67-81.
    • (1881) Oeuvres Complètes , vol.2 , pp. 67-81
    • Abel, N.1
  • 5
    • 0008960517 scopus 로고
    • The Poisson process with a curved absorbing boundary
    • DANIELS, H. E. (1963) The Poisson process with a curved absorbing boundary. Bull. Int. Statist, Inst., 34th session. 40, 994-1008.
    • (1963) Bull. Int. Statist, Inst., 34th Session , vol.40 , pp. 994-1008
    • Daniels, H.E.1
  • 7
    • 3142537781 scopus 로고
    • Asymptotic absorption probabilities for a Poisson process
    • GALLOT, S. F. L. (1966) Asymptotic absorption probabilities for a Poisson process. J. Appl. Prob. 3, 445-452.
    • (1966) J. Appl. Prob. , vol.3 , pp. 445-452
    • Gallot, S.F.L.1
  • 8
    • 21344478461 scopus 로고
    • Absorption and first passage times for a compound Poisson process in a general upper boundary
    • GALLOT, S. F. L. (1993) Absorption and first passage times for a compound Poisson process in a general upper boundary. J. Appl. Prob. 30, 835-850.
    • (1993) J. Appl. Prob. , vol.30 , pp. 835-850
    • Gallot, S.F.L.1
  • 9
    • 0002839739 scopus 로고
    • Recherches sur les dérivées successives des fonctions analytiques. Généralisation de la série d'Abel
    • GONTCHAROFF, W. (1930) Recherches sur les dérivées successives des fonctions analytiques. Généralisation de la série d'Abel. Ann. Sci. Ecole Normale Sup. 47, 1-78.
    • (1930) Ann. Sci. Ecole Normale Sup. , vol.47 , pp. 1-78
    • Gontcharoff, W.1
  • 10
    • 3142635890 scopus 로고
    • Appell polynomials
    • ed. M. Hazewinkel. Kluwer, Dordrecht
    • KAZ'MIN, Y. A. (1988) Appell polynomials. In Encyclopedia of Mathematics, ed. M. Hazewinkel. Kluwer, Dordrecht, pp. 1, 209-210.
    • (1988) Encyclopedia of Mathematics , pp. 1
    • Kaz'min, Y.A.1
  • 11
    • 25744458767 scopus 로고
    • Quelques nouvelles classes de distributions engendrées par des familles de polynômes non-standards
    • LEFÈVRE, CL. AND PICARD, PH. (1989) Quelques nouvelles classes de distributions engendrées par des familles de polynômes non-standards. Bull. Int. Statist. Inst., 47th session. 2, 32-33.
    • (1989) Bull. Int. Statist. Inst., 47th Session , vol.2 , pp. 32-33
    • Lefèvre, Cl.1    Picard, Ph.2
  • 12
    • 0002708819 scopus 로고
    • A non-standard family of polynomials and the final size distribution of Reed-Frost epidemic processes
    • LEFÈVRE, CL. AND PICARD, PH. (1990) A non-standard family of polynomials and the final size distribution of Reed-Frost epidemic processes. Adv. Appl. Prob. 22, 25-48.
    • (1990) Adv. Appl. Prob. , vol.22 , pp. 25-48
    • Lefèvre, Cl.1    Picard, Ph.2
  • 13
    • 0009123751 scopus 로고    scopus 로고
    • Abelian-type expansions and non-linear death processes (II)
    • LEFÈVRE, CL. AND PICARD, PH. (1996) Abelian-type expansions and non-linear death processes (II). Adv. Appl. Prob. 28, 877-894.
    • (1996) Adv. Appl. Prob. , vol.28 , pp. 877-894
    • Lefèvre, Cl.1    Picard, Ph.2
  • 14
    • 0002934845 scopus 로고    scopus 로고
    • On the foundations of combinatorial theory - III: Theory of binomial enumeration
    • Academic Press, New York
    • MULLIN, R. AND ROTA, G.-C. On the foundations of combinatorial theory - III: Theory of binomial enumeration. In Graph Theory and its Applications. Academic Press, New York, pp 167-213.
    • Graph Theory and Its Applications , pp. 167-213
    • Mullin, R.1    Rota, G.-C.2
  • 15
    • 0001102170 scopus 로고
    • Sheffer polynomials for computing exact Kolmogorov-Smirnov and Rényi type distributions
    • NIEDERHAUSEN, H. (1981) Sheffer polynomials for computing exact Kolmogorov-Smirnov and Rényi type distributions. Ann. Statist. 9, 923-944.
    • (1981) Ann. Statist. , vol.9 , pp. 923-944
    • Niederhausen, H.1
  • 16
    • 84884714583 scopus 로고
    • Sheffer polynomials
    • ed. S. Kotz, N. Johnson and C. Read. Wiley, New York
    • NIEDERHAUSEN, H. (1988) Sheffer polynomials. In Encyclopedia of Statistical Sciences, ed. S. Kotz, N. Johnson and C. Read. Wiley, New York, pp 8, 436-441.
    • (1988) Encyclopedia of Statistical Sciences , pp. 8
    • Niederhausen, H.1
  • 17
    • 0002035606 scopus 로고
    • Applications of martingale theory to some epidemic models
    • PICARD, PH. (1980) Applications of martingale theory to some epidemic models. J. Appl. Prob. 17, 583-599.
    • (1980) J. Appl. Prob. , vol.17 , pp. 583-599
    • Picard, Ph.1
  • 18
    • 3142646119 scopus 로고
    • Sur des familles de polynômes non-standards intervenant dans des problèmes de premier passage
    • PICARD, PH. AND LEFÈVRE, CL. (1989) Sur des familles de polynômes non-standards intervenant dans des problèmes de premier passage. Bull. Int. Statist. Inst., 47th session. 2, 208-209.
    • (1989) Bull. Int. Statist. Inst., 47th Session , vol.2 , pp. 208-209
    • Picard, Ph.1    Lefèvre, Cl.2
  • 19
    • 0000729953 scopus 로고
    • A unified analysis of the final size and severity distribution in collective Reed-Frost epidemic processes
    • PICARD, PH. AND LEFèVRE, CL. (1990) A unified analysis of the final size and severity distribution in collective Reed-Frost epidemic processes. Adv. Appl. Prob. 22, 269-294.
    • (1990) Adv. Appl. Prob. , vol.22 , pp. 269-294
    • Picard, Ph.1    Lefèvre, Cl.2
  • 20
    • 38149147469 scopus 로고
    • On the first crossing of the surplus process with a given upper barrier
    • PICARD, PH. AND LEFèVRE, CL. (1994) On the first crossing of the surplus process with a given upper barrier. Insurance: Math. Ecort. 14, 163-179.
    • (1994) Insurance: Math. Ecort. , vol.14 , pp. 163-179
    • Picard, Ph.1    Lefèvre, Cl.2
  • 21
    • 38249002977 scopus 로고
    • On hitting times for jump-diffusion processes with past dependent local characteristics
    • SCHÄL, M. (1993) On hitting times for jump-diffusion processes with past dependent local characteristics. Stoch. Proc. Appl. 47, 131-142.
    • (1993) Stoch. Proc. Appl. , vol.47 , pp. 131-142
    • Schäl, M.1
  • 22
    • 84972535289 scopus 로고
    • Some properties of polynomial sets of type zero
    • SHEFFER, I. M. (1939) Some properties of polynomial sets of type zero. Duke Math. J. 5, 590-622.
    • (1939) Duke Math. J. , vol.5 , pp. 590-622
    • Sheffer, I.M.1
  • 23
    • 0001770263 scopus 로고
    • Distribution of first-exit times for empirical counting and Poisson processes with moving boundaries
    • STADJE, W. (1993) Distribution of first-exit times for empirical counting and Poisson processes with moving boundaries. Commun. Statist. Stoch. Models 9, 91-103.
    • (1993) Commun. Statist. Stoch. Models , vol.9 , pp. 91-103
    • Stadje, W.1
  • 24
    • 0012981382 scopus 로고
    • Some exact results for one-sided distribution tests of the Kolmogorov-Smirnov type
    • WHITTLE, P. (1961) Some exact results for one-sided distribution tests of the Kolmogorov-Smirnov type. Ann. Math. Statist. 32, 499-505.
    • (1961) Ann. Math. Statist. , vol.32 , pp. 499-505
    • Whittle, P.1
  • 25
    • 0000585763 scopus 로고
    • Distributions of stopping times for Poisson processes with linear boundaries
    • ZACKS, S. (1991) Distributions of stopping times for Poisson processes with linear boundaries. Commun. Statist. Stoch. Models 7, 233-242.
    • (1991) Commun. Statist. Stoch. Models , vol.7 , pp. 233-242
    • Zacks, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.