메뉴 건너뛰기




Volumn 253, Issue 2, 2001, Pages 515-531

Orthogonal Polynomials in Stein's Method

Author keywords

Approximation; Distributions; Markov processes; Orthogonal polynomials; Pearson's class, Ord's class; Stein's method

Indexed keywords


EID: 0035863994     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7159     Document Type: Article
Times cited : (43)

References (22)
  • 2
    • 0004167330 scopus 로고    scopus 로고
    • Encyclopedia of Mathematics and Its Applications. Cambridge: Cambridge Univ. Press
    • Andrews G. E., Askey R., Roy R. Special Functions. Encyclopedia of Mathematics and Its Applications. 71:1999;Cambridge Univ. Press, Cambridge.
    • (1999) Special Functions , vol.71
    • Andrews, G.E.1    Askey, R.2    Roy, R.3
  • 3
    • 0007084383 scopus 로고
    • Equilibrium distributions for Markov population processes
    • Barbour A. D. Equilibrium distributions for Markov population processes. Adv. Appl. Probab. 12:1980;591-614.
    • (1980) Adv. Appl. Probab. , vol.12 , pp. 591-614
    • Barbour, A.D.1
  • 4
    • 0001077489 scopus 로고
    • Stein's method and Poisson process convergence
    • Barbour A. D. Stein's method and Poisson process convergence. J. Appl. Probab. A. 25:1988;175-184.
    • (1988) J. Appl. Probab. A , vol.25 , pp. 175-184
    • Barbour, A.D.1
  • 5
    • 0000499854 scopus 로고
    • Stein's method for diffusion approximations
    • Barbour A. D. Stein's method for diffusion approximations. Probab. Theory Related Fields. 84:1990;297-322.
    • (1990) Probab. Theory Related Fields , vol.84 , pp. 297-322
    • Barbour, A.D.1
  • 8
    • 0001067389 scopus 로고
    • Poisson approximation for dependent trials
    • Chen L. H. Y. Poisson approximation for dependent trials. Ann. Probab. 22:1975;1607-1618.
    • (1975) Ann. Probab. , vol.22 , pp. 1607-1618
    • Chen, L.H.Y.1
  • 10
    • 84972535617 scopus 로고
    • Closed form summation for classical distributions: Variations on a theme of de Moivre
    • Diaconis P., Zabell S. Closed form summation for classical distributions: Variations on a theme of de Moivre. Statist. Sci. 6:1991;284-302.
    • (1991) Statist. Sci. , vol.6 , pp. 284-302
    • Diaconis, P.1    Zabell, S.2
  • 11
    • 0000007742 scopus 로고
    • Systems of polynomials connected with Charlier expansions and the Pearson differential and difference equation
    • Hildebrandt E. H. Systems of polynomials connected with Charlier expansions and the Pearson differential and difference equation. Ann. Math. Statist. 2:1931;379-439.
    • (1931) Ann. Math. Statist. , vol.2 , pp. 379-439
    • Hildebrandt, E.H.1
  • 13
    • 0000036102 scopus 로고
    • The differential equations of birth-and-death processes, and the Stieltjes moment problem
    • Karlin S., McGregor J. L. The differential equations of birth-and-death processes, and the Stieltjes moment problem. Trans. Amer. Math. Soc. 85:1957;489-546.
    • (1957) Trans. Amer. Math. Soc. , vol.85 , pp. 489-546
    • Karlin, S.1    McGregor, J.L.2
  • 16
    • 0001475647 scopus 로고
    • Spectral theory for the differential equations of simple birth and death processes
    • Ledermann W., Reuter G. E. H. Spectral theory for the differential equations of simple birth and death processes. Philos. Trans. Roy. Soc. London Ser. A. 246:1954;321-369.
    • (1954) Philos. Trans. Roy. Soc. London Ser. A , vol.246 , pp. 321-369
    • Ledermann, W.1    Reuter, G.E.H.2
  • 20
    • 0000457248 scopus 로고
    • A bound for the error in the normal approximation to the distibution of a sum of dependent random variables
    • Berkeley: Univ. of California Press. p. 583-602
    • Stein C. A bound for the error in the normal approximation to the distibution of a sum of dependent random variables. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 1972;Univ. of California Press, Berkeley. p. 583-602.
    • (1972) Proc. Sixth Berkeley Symp. Math. Statist. Probab
    • Stein, C.1
  • 22
    • 0007137107 scopus 로고    scopus 로고
    • Spectral representation of four finite birth and death processes
    • Van Assche W., Parthasarathy P. R., Lenin R. B. Spectral representation of four finite birth and death processes. Math. Sci. 24:1999;105-112.
    • (1999) Math. Sci. , vol.24 , pp. 105-112
    • Van Assche, W.1    Parthasarathy, P.R.2    Lenin, R.B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.