메뉴 건너뛰기




Volumn 110, Issue 2, 2004, Pages 177-245

Functional limit theorems for multitype branching processes and generalized Pólya urns

Author keywords

Generalized Polya urns; Multitype branching processes; Urn models

Indexed keywords


EID: 1542288384     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2003.12.002     Document Type: Article
Times cited : (299)

References (58)
  • 2
    • 84967773316 scopus 로고
    • Almost sure behavior of linear functionals of supercritical branching processes
    • Asmussen S. Almost sure behavior of linear functionals of supercritical branching processes Trans. Amer. Math. Soc. 231 1 1977 233-248
    • (1977) Trans. Amer. Math. Soc. , vol.231 , Issue.1 , pp. 233-248
    • Asmussen, S.1
  • 3
    • 0344668851 scopus 로고
    • Some results on multitype continuous time Markov branching processes
    • Athreya K.B. Some results on multitype continuous time Markov branching processes Ann. Math. Statist. 39 1968 347-357
    • (1968) Ann. Math. Statist. , vol.39 , pp. 347-357
    • Athreya, K.B.1
  • 4
    • 0011623470 scopus 로고
    • Limit theorems for multitype continuous time Markov branching processes. I. The case of an eigenvector linear functional
    • Athreya K.B. Limit theorems for multitype continuous time Markov branching processes. I. The case of an eigenvector linear functional Z. Wahrsch. Verw. Gebiete 12 1969 320-332
    • (1969) Z. Wahrsch. Verw. Gebiete , vol.12 , pp. 320-332
    • Athreya, K.B.1
  • 5
    • 0011560561 scopus 로고
    • Limit theorems for multitype continuous time Markov branching processes. II. The case of an arbitrary linear functional
    • Athreya K.B. Limit theorems for multitype continuous time Markov branching processes. II. The case of an arbitrary linear functional Z. Wahrsch. Verw. Gebiete 13 1969 204-214
    • (1969) Z. Wahrsch. Verw. Gebiete , vol.13 , pp. 204-214
    • Athreya, K.B.1
  • 6
    • 0001431180 scopus 로고
    • Limit theorems for the split times of branching processes
    • Athreya K.B. Karlin S. Limit theorems for the split times of branching processes J. Math. Mech. 17 1967 257-277
    • (1967) J. Math. Mech. , vol.17 , pp. 257-277
    • Athreya, K.B.1    Karlin, S.2
  • 7
    • 0001625953 scopus 로고
    • Embedding of urn schemes into continuous time Markov branching processes and related limit theorems
    • Athreya K.B. Karlin S. Embedding of urn schemes into continuous time Markov branching processes and related limit theorems Ann. Math. Statist. 39 1968 1801-1817
    • (1968) Ann. Math. Statist. , vol.39 , pp. 1801-1817
    • Athreya, K.B.1    Karlin, S.2
  • 9
    • 0000167348 scopus 로고
    • Asymptotic normality in the generalized Pólya-Eggenberger urn model, with an application to computer data structures
    • Bagchi A. Pal A.K. Asymptotic normality in the generalized Pólya-Eggenberger urn model, with an application to computer data structures SIAM J. Algebraic Discrete Methods 6 3 1985 394-405
    • (1985) SIAM J. Algebraic Discrete Methods , vol.6 , Issue.3 , pp. 394-405
    • Bagchi, A.1    Pal, A.K.2
  • 10
    • 0003143199 scopus 로고    scopus 로고
    • Asymptotic theorems for urn models with nonhomogeneous generating matrices
    • Bai Z.D. Hu F. Asymptotic theorems for urn models with nonhomogeneous generating matrices Stochastic Process. Appl. 80 1 1999 87-101
    • (1999) Stochastic Process. Appl. , vol.80 , Issue.1 , pp. 87-101
    • Bai, Z.D.1    Hu, F.2
  • 11
    • 0036439332 scopus 로고    scopus 로고
    • Gaussian approximation theorems for urn models and their applications
    • Bai Z.D. Hu F. Zhang L.-X. Gaussian approximation theorems for urn models and their applications Ann. Appl. Probab. 12 4 2002 1149-1173
    • (2002) Ann. Appl. Probab. , vol.12 , Issue.4 , pp. 1149-1173
    • Bai, Z.D.1    Hu, F.2    Zhang, L.-X.3
  • 12
    • 1542281988 scopus 로고
    • Nouvelles applications des grandeurs aléatoires presqu'indépendantes
    • Bernstein S. Nouvelles applications des grandeurs aléatoires presqu'indépendantes Izv. Akad. Nauk SSSR Ser. Mat. 4 1940 137-150
    • (1940) Izv. Akad. Nauk SSSR Ser. Mat. , vol.4 , pp. 137-150
    • Bernstein, S.1
  • 13
    • 0009238477 scopus 로고
    • Sur un problème du schéma des urnes à composition variable
    • Bernstein S. Sur un problème du schéma des urnes à composition variable C. R. (Doklady) Acad. Sci. URSS (N.S.) 28 1940 5-7
    • (1940) C. R. (Doklady) Acad. Sci. URSS (N.S.) , vol.28 , pp. 5-7
    • Bernstein, S.1
  • 15
    • 1542312119 scopus 로고    scopus 로고
    • M-ary search trees when m≥ 27: A strong asymptotics for the space requirements
    • To appear. Available from
    • Chauvin, B., Pouyanne, N., 2004. m-ary search trees when m≥ 27: a strong asymptotics for the space requirements. Random Struct. Algorithms, to appear. Available from http://www.math.uvsq.fr/~chauvin/publis.html
    • (2004) Random Struct. Algorithms
    • Chauvin, B.1    Pouyanne, N.2
  • 16
    • 0035539863 scopus 로고    scopus 로고
    • Phase changes in random m-ary search trees and generalized quicksort
    • Chern H.-H. Hwang H.-K. Phase changes in random m-ary search trees and generalized quicksort Random Struct. Algorithms 19 3-4 2001 316-358
    • (2001) Random Struct. Algorithms , vol.19 , Issue.3-4 , pp. 316-358
    • Chern, H.-H.1    Hwang, H.-K.2
  • 18
    • 1542312122 scopus 로고    scopus 로고
    • Transfer theorems and asymptotic distributional results for m-ary search trees
    • Preprint. Available from
    • Fill, J., Kapur, N., 2003. Transfer theorems and asymptotic distributional results for m-ary search trees. Preprint. Available from http://www.mts.jhu.edu/~fill/
    • (2003)
    • Fill, J.1    Kapur, N.2
  • 20
  • 22
    • 0010774666 scopus 로고
    • Martingale functional central limit theorems for a generalized Pólya urn
    • Gouet R. Martingale functional central limit theorems for a generalized Pólya urn Ann. Probab. 21 3 1993 1624-1639
    • (1993) Ann. Probab. , vol.21 , Issue.3 , pp. 1624-1639
    • Gouet, R.1
  • 24
    • 0000638015 scopus 로고
    • The limiting behaviour of certain stopped sums and some applications
    • Gut A. Janson S. The limiting behaviour of certain stopped sums and some applications Scand. J. Statist. 10 1983 281-292
    • (1983) Scand. J. Statist. , vol.10 , pp. 281-292
    • Gut, A.1    Janson, S.2
  • 25
    • 0038336151 scopus 로고    scopus 로고
    • Second phase changes in random m-ary search trees and generalized quicksort: Convergence rates
    • Hwang H.-K. Second phase changes in random m-ary search trees and generalized quicksort: convergence rates Ann. Probab. 31 2 2003 609-629
    • (2003) Ann. Probab. , vol.31 , Issue.2 , pp. 609-629
    • Hwang, H.-K.1
  • 27
    • 1542342278 scopus 로고
    • Limit theorems for certain branching random walks on compact groups and homogeneous spaces
    • Janson S. Limit theorems for certain branching random walks on compact groups and homogeneous spaces Ann. Probab. 11 1983 909-930
    • (1983) Ann. Probab. , vol.11 , pp. 909-930
    • Janson, S.1
  • 28
    • 84990634533 scopus 로고
    • A functional limit theorem for random graphs with applications to subgraph count statistics
    • Janson S. A functional limit theorem for random graphs with applications to subgraph count statistics Random Struct. Algorithms 1 1990 15-37
    • (1990) Random Struct. Algorithms , vol.1 , pp. 15-37
    • Janson, S.1
  • 29
    • 0013487388 scopus 로고
    • Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics
    • Providence, RI: American Mathematical Society
    • Janson S. Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics Mem. Amer. Math. Soc. Vol. 111(534) 1994 American Mathematical Society Providence, RI
    • (1994) Mem. Amer. Math. Soc. , vol.111 , Issue.534
    • Janson, S.1
  • 31
    • 26544465216 scopus 로고    scopus 로고
    • Asymptotic degree distribution in random recursive trees
    • Preprint. Available from
    • Janson, S., 2003. Asymptotic degree distribution in random recursive trees. Preprint. Available from http://www.math.uu.se/~svante/
    • (2003)
    • Janson, S.1
  • 35
    • 0002610091 scopus 로고
    • Additional limit theorems for indecomposable multidimensional Galton-Watson processes
    • Kesten H. Stigum B.P. Additional limit theorems for indecomposable multidimensional Galton-Watson processes Ann. Math. Statist. 37 1966 1463-1481
    • (1966) Ann. Math. Statist. , vol.37 , pp. 1463-1481
    • Kesten, H.1    Stigum, B.P.2
  • 36
    • 0001552596 scopus 로고
    • Limit theorems for decomposable multi-dimensional Galton-Watson processes
    • Kesten H. Stigum B.P. Limit theorems for decomposable multi-dimensional Galton-Watson processes J. Math. Anal. Appl. 17 1967 309-338
    • (1967) J. Math. Anal. Appl. , vol.17 , pp. 309-338
    • Kesten, H.1    Stigum, B.P.2
  • 38
    • 0028516486 scopus 로고
    • The joint distribution of elastic buckets in multiway search trees
    • Lew W. Mahmoud H.M. The joint distribution of elastic buckets in multiway search trees SIAM J. Comput. 23 5 1994 1050-1074
    • (1994) SIAM J. Comput. , vol.23 , Issue.5 , pp. 1050-1074
    • Lew, W.1    Mahmoud, H.M.2
  • 39
    • 0001407755 scopus 로고
    • Weak convergence of probability measures and random functions in the function space D(0,∞)
    • Lindvall T. Weak convergence of probability measures and random functions in the function space D(0,∞) J. Appl. Probab. 10 1973 109-121
    • (1973) J. Appl. Probab. , vol.10 , pp. 109-121
    • Lindvall, T.1
  • 41
    • 0002932874 scopus 로고    scopus 로고
    • On rotations in fringe-balanced binary trees
    • Mahmoud H.M. On rotations in fringe-balanced binary trees Inform. Process. Lett. 65 1 1998 41-46
    • (1998) Inform. Process. Lett. , vol.65 , Issue.1 , pp. 41-46
    • Mahmoud, H.M.1
  • 42
    • 26544452745 scopus 로고    scopus 로고
    • Urn models evolving by drawing multisets of balls
    • Preprint
    • Mahmoud, H.M., 2000. Urn models evolving by drawing multisets of balls. Preprint.
    • (2000)
    • Mahmoud, H.M.1
  • 43
    • 0038095765 scopus 로고    scopus 로고
    • The size of random bucket trees via urn models
    • Mahmoud H.M. The size of random bucket trees via urn models Acta Inform. 38 11-12 2002 813-838
    • (2002) Acta Inform. , vol.38 , Issue.11-12 , pp. 813-838
    • Mahmoud, H.M.1
  • 44
    • 0002716965 scopus 로고
    • Analysis of the space of search trees under the random insertion algorithm
    • Mahmoud H.M. Pittel B. Analysis of the space of search trees under the random insertion algorithm J. Algorithms 10 1 1989 52-75
    • (1989) J. Algorithms , vol.10 , Issue.1 , pp. 52-75
    • Mahmoud, H.M.1    Pittel, B.2
  • 45
    • 84990634444 scopus 로고
    • Asymptotic joint normality of outdegrees of nodes in random recursive trees
    • Mahmoud H.M. Smythe R.T. Asymptotic joint normality of outdegrees of nodes in random recursive trees Random Struct. Algorithms 3 3 1992 255-266
    • (1992) Random Struct. Algorithms , vol.3 , Issue.3 , pp. 255-266
    • Mahmoud, H.M.1    Smythe, R.T.2
  • 46
    • 84990634414 scopus 로고
    • On the structure of random plane-oriented recursive trees and their branches
    • Mahmoud H.M. Smythe R.T. Szymański J. On the structure of random plane-oriented recursive trees and their branches Random Struct. Algorithms 4 2 1993 151-176
    • (1993) Random Struct. Algorithms , vol.4 , Issue.2 , pp. 151-176
    • Mahmoud, H.M.1    Smythe, R.T.2    Szymański, J.3
  • 47
    • 0006061726 scopus 로고
    • Recursive trees with no nodes of out-degree one
    • Meir A. Moon J.W. Recursive trees with no nodes of out-degree one Congr. Numer. 66 1988 49-62
    • (1988) Congr. Numer. , vol.66 , pp. 49-62
    • Meir, A.1    Moon, J.W.2
  • 49
    • 0001453215 scopus 로고
    • Sur quelques points de la théorie des probabilités
    • Pólya G. Sur quelques points de la théorie des probabilités Ann. Inst. Poincaré 1 1931 117-161
    • (1931) Ann. Inst. Poincaré , vol.1 , pp. 117-161
    • Pólya, G.1
  • 50
    • 0003220764 scopus 로고
    • Stochastic Integration and Differential Equations. A New Approach
    • Berlin: Springer
    • Protter P. Stochastic Integration and Differential Equations. A New Approach Applications of Mathematics Vol. 21 1990 Springer Berlin
    • (1990) Applications of Mathematics , vol.21
    • Protter, P.1
  • 54
    • 0030582793 scopus 로고    scopus 로고
    • Central limit theorems for urn models
    • Smythe R.T. Central limit theorems for urn models Stochastic Process. Appl. 65 1 1996 115-137
    • (1996) Stochastic Process. Appl. , vol.65 , Issue.1 , pp. 115-137
    • Smythe, R.T.1
  • 55
    • 0011560562 scopus 로고
    • Play-the-winner designs, generalized Pólya urns, and Markov branching processes
    • N. Flournoy, & W. F. Rosenberger (Eds.), Hayward, CA: Inst. Math. Statist
    • Smythe R.T. Rosenberger W.F. Play-the-winner designs, generalized Pólya urns, and Markov branching processes In: Flournoy N. Rosenberger W.F. (Eds.), Adaptive Designs IMS Lecture Notes Monograph Ser. Vol. 25 1995 13-22 Inst. Math. Statist. Hayward, CA-
    • (1995) Adaptive Designs , vol.25 , pp. 13-22
    • Smythe, R.T.1    Rosenberger, W.F.2
  • 56
    • 0242333232 scopus 로고    scopus 로고
    • A limit law for outputs in random recursive circuits
    • Tsukiji T. Mahmoud H. A limit law for outputs in random recursive circuits Algorithmica 31 3 2001 403-412
    • (2001) Algorithmica , vol.31 , Issue.3 , pp. 403-412
    • Tsukiji, T.1    Mahmoud, H.2
  • 57
    • 84950622103 scopus 로고
    • The randomized play-the-winner rule in medical trials
    • Wei L.J. Durham S. The randomized play-the-winner rule in medical trials J. Amer. Statist. Assoc. 73 364 1978 840-843
    • (1978) J. Amer. Statist. Assoc. , vol.73 , Issue.364 , pp. 840-843
    • Wei, L.J.1    Durham, S.2
  • 58
    • 0001169395 scopus 로고
    • Statistical inference with data-dependent treatment allocation rules
    • Wei L.J. Smythe R.T. Lin D.Y. Park T.S. Statistical inference with data-dependent treatment allocation rules J. Amer. Statist. Assoc. 85 409 1990 156-162
    • (1990) J. Amer. Statist. Assoc. , vol.85 , Issue.409 , pp. 156-162
    • Wei, L.J.1    Smythe, R.T.2    Lin, D.Y.3    Park, T.S.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.