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Volumn 33, Issue 4, 2005, Pages 1422-1451

Donsker theorems for diffusions: Necessary and sufficient conditions

Author keywords

Continuous martingales; Diffusions; Donsker class; Local time; Local time estimator; Majorizing measures; Uniform central limit theorem

Indexed keywords


EID: 16244414130     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117905000000152     Document Type: Article
Times cited : (26)

References (30)
  • 1
    • 23244459337 scopus 로고
    • The central limit theorem for stochastic processes. II
    • ANDERSEN, N. T. and DOBRIĆ, V. (1988). The central limit theorem for stochastic processes. II. J. Theoret. Probab. 1 287-303.
    • (1988) J. Theoret. Probab. , vol.1 , pp. 287-303
    • Andersen, N.T.1    Dobrić, V.2
  • 2
    • 23244452463 scopus 로고
    • A uniform CLT for continuous martingales
    • BAE, J. and LEVENTAL, S. (1995). A uniform CLT for continuous martingales. J. Korean Statist. Soc. 24 225-231.
    • (1995) J. Korean Statist. Soc. , vol.24 , pp. 225-231
    • Bae, J.1    Levental, S.2
  • 3
    • 0040125256 scopus 로고
    • On the functional central limit theorem and the law of the iterated logarithm for Markov processes
    • BHATTACHARYA, R. N. (1982). On the functional central limit theorem and the law of the iterated logarithm for Markov processes. Z. Wahrsch. Verw. Gebiete 60 185-201.
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.60 , pp. 185-201
    • Bhattacharya, R.N.1
  • 4
    • 0842320798 scopus 로고    scopus 로고
    • Local time and density estimation in continuous time
    • BOSQ, D. and DAVYDOV, Y. (1999). Local time and density estimation in continuous time. Math. Methods Statist. 8 22-45.
    • (1999) Math. Methods Statist. , vol.8 , pp. 22-45
    • Bosq, D.1    Davydov, Y.2
  • 5
    • 0000660999 scopus 로고
    • The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
    • DUDLEY, R. M. (1967). The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal. 1 290-330.
    • (1967) J. Funct. Anal. , vol.1 , pp. 290-330
    • Dudley, R.M.1
  • 8
    • 0002501936 scopus 로고
    • Lectures on the central limit theorem for empirical processes
    • Springer, New York
    • GINÉ, E. and ZINN, J. (1986). Lectures on the central limit theorem for empirical processes. Probability and Banach Spaces. Lecture Notes in Math. 1221 50-113. Springer, New York.
    • (1986) Probability and Banach Spaces. Lecture Notes in Math. , vol.1221 , pp. 50-113
    • Giné, E.1    Zinn, J.2
  • 13
    • 0010041965 scopus 로고    scopus 로고
    • Efficiency of the empirical distribution for ergodic diffusion
    • KUTOYANTS, YU. A. (1997). Efficiency of the empirical distribution for ergodic diffusion. Bernoulli 3 445-456.
    • (1997) Bernoulli , vol.3 , pp. 445-456
    • Kutoyants, Yu.A.1
  • 14
    • 0041862180 scopus 로고    scopus 로고
    • Efficient density estimation for ergodic diffusion processes
    • KUTOYANTS, YU. A. (1998). Efficient density estimation for ergodic diffusion processes. Statist. Inference Stochast. Process. 1 131-155.
    • (1998) Statist. Inference Stochast. Process. , vol.1 , pp. 131-155
    • Kutoyants, Yu.A.1
  • 15
    • 0036347749 scopus 로고    scopus 로고
    • 2 efficiency of an empiric distribution for ergodic diffusion processes
    • 2 efficiency of an empiric distribution for ergodic diffusion processes. Theory Probab. Appl. 46 140-146.
    • (2001) Theory Probab. Appl. , vol.46 , pp. 140-146
    • Kutoyants, Yu.A.1    Negri, I.2
  • 18
    • 0009966945 scopus 로고    scopus 로고
    • Stationary distribution function estimation for ergodic diffusion process
    • NEGRI, I. (1998). Stationary distribution function estimation for ergodic diffusion process. Statist. Inference Stochast. Process. 1 61-84.
    • (1998) Statist. Inference Stochast. Process. , vol.1 , pp. 61-84
    • Negri, I.1
  • 19
    • 0041364646 scopus 로고    scopus 로고
    • On efficient estimation of invariant density for ergodic diffusion processes
    • NEGRI, I. (2001). On efficient estimation of invariant density for ergodic diffusion processes. Statist. Probab. Lett. 51 79-85.
    • (2001) Statist. Probab. Lett. , vol.51 , pp. 79-85
    • Negri, I.1
  • 20
    • 0002154328 scopus 로고    scopus 로고
    • ∞-valued semimartingales and their applications
    • ∞-valued semimartingales and their applications. Probab. Theory Related Fields 108 459-494.
    • (1997) Probab. Theory Related Fields , vol.108 , pp. 459-494
    • Nishiyama, Y.1
  • 21
    • 0033472042 scopus 로고    scopus 로고
    • A maximal inequality for continuous martingales and M-estimation in a Gaussian white noise model
    • NISHIYAMA, Y. (1999). A maximal inequality for continuous martingales and M-estimation in a Gaussian white noise model. Ann. Statist. 27 675-696.
    • (1999) Ann. Statist. , vol.27 , pp. 675-696
    • Nishiyama, Y.1
  • 27
    • 0002883222 scopus 로고
    • A simple proof of the majorizing measure theorem
    • TALAGRAND, M. (1992). A simple proof of the majorizing measure theorem. Geom. Funct. Anal. 2 118-125.
    • (1992) Geom. Funct. Anal. , vol.2 , pp. 118-125
    • Talagrand, M.1
  • 28
    • 0001957366 scopus 로고
    • Sharper bounds for Gaussian and empirical processes
    • TALAGRAND, M. (1995). Sharper bounds for Gaussian and empirical processes. Ann. Probab. 22 28-76.
    • (1995) Ann. Probab. , vol.22 , pp. 28-76
    • Talagrand, M.1
  • 30
    • 23244446675 scopus 로고    scopus 로고
    • On uniform laws of large numbers for ergodic diffusions and consistency of estimators
    • VAN ZANTEN, J. H. (2003). On uniform laws of large numbers for ergodic diffusions and consistency of estimators. Statist. Inference Stochast. Process. 6 199-213.
    • (2003) Statist. Inference Stochast. Process. , vol.6 , pp. 199-213
    • Van Zanten, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.