메뉴 건너뛰기




Volumn 19, Issue 1, 2006, Pages 1-44

An asymptotic expansion for probabilities of moderate deviations for multivariate martingales

Author keywords

Martingales; Moderate deviations; Rate of convergence

Indexed keywords


EID: 33747830149     PISSN: 08949840     EISSN: 15729230     Source Type: Journal    
DOI: 10.1007/s10959-006-0001-x     Document Type: Article
Times cited : (23)

References (26)
  • 1
    • 0040977035 scopus 로고
    • Limit theorems for probabilities of moderate deviations
    • in Russian
    • Amosova, N. N. (1972). Limit theorems for probabilities of moderate deviations. Vestnik Leningrad. Univ. 13, 5-14 (in Russian).
    • (1972) Vestnik Leningrad. Univ. , vol.13 , pp. 5-14
    • Amosova, N.N.1
  • 2
    • 0039215706 scopus 로고
    • On the central limit theorem
    • Bergström, H. (1944). On the central limit theorem. Skand. Aktuarietidskr. 27, 139-153.
    • (1944) Skand. Aktuarietidskr. , vol.27 , pp. 139-153
    • Bergström, H.1
  • 4
    • 0000963887 scopus 로고
    • Exact convergence rates in some martingale central limit theorems
    • Bolthausen, E. (1982). Exact convergence rates in some martingale central limit theorems. Ann. Probab. 10, 672-688.
    • (1982) Ann. Probab. , vol.10 , pp. 672-688
    • Bolthausen, E.1
  • 5
    • 0040771728 scopus 로고
    • Certain non-uniform rates of convergence to normality for a restricted class of martingales
    • Bose, A. (1986). Certain non-uniform rates of convergence to normality for a restricted class of martingales. Stochastics 16, 279-294.
    • (1986) Stochastics , vol.16 , pp. 279-294
    • Bose, A.1
  • 7
    • 0001846814 scopus 로고    scopus 로고
    • Moderate deviations for martingales with bounded jumps
    • Dembo, A. (1996). Moderate deviations for martingales with bounded jumps. Elec. Comm. Probab. 1, 11-17.
    • (1996) Elec. Comm. Probab. , vol.1 , pp. 11-17
    • Dembo, A.1
  • 8
    • 33747819431 scopus 로고    scopus 로고
    • Moderate deviations for martingale differences and applications to Φ-mixing sequences
    • Djellout, H. (2002). Moderate deviations for martingale differences and applications to Φ-mixing sequences. Stock. Stock. Rep. 73, 37-63.
    • (2002) Stock. Stock. Rep. , vol.73 , pp. 37-63
    • Djellout, H.1
  • 9
    • 0030076763 scopus 로고    scopus 로고
    • Moderate deviations for martingales and mixing random processes
    • Gao, F.-Q. (1996). Moderate deviations for martingales and mixing random processes. Stock Processes Appl. 61, 263-275.
    • (1996) Stock Processes Appl. , vol.61 , pp. 263-275
    • Gao, F.-Q.1
  • 10
    • 0040177511 scopus 로고
    • On the rate of convergence in the central limit theorem for d-dimensional semimartingales
    • Grama, I. G. (1993). On the rate of convergence in the central limit theorem for d-dimensional semimartingales. Stock. Stock. Rep. 44, 131-152.
    • (1993) Stock. Stock. Rep. , vol.44 , pp. 131-152
    • Grama, I.G.1
  • 11
    • 0031513809 scopus 로고    scopus 로고
    • On moderate deviations for martingales
    • Grama, I. G. (1997). On moderate deviations for martingales. Ann. Probab. 25, 152-183.
    • (1997) Ann. Probab. , vol.25 , pp. 152-183
    • Grama, I.G.1
  • 12
    • 33747864381 scopus 로고
    • An estimation of the rate of convergence in CLT for dependent two-dimensional random vectors
    • in Russian
    • Gudynas, P. (1988). An estimation of the rate of convergence in CLT for dependent two-dimensional random vectors. Liet. Matem. Rink. 28, 66-76 (in Russian).
    • (1988) Liet. Matem. Rink. , vol.28 , pp. 66-76
    • Gudynas, P.1
  • 13
    • 33747858621 scopus 로고
    • An estimation of the convergence rate in CLT for dependent random elements in Hubert space
    • in Russian
    • Gudynas, P. (1991). An estimation of the convergence rate in CLT for dependent random elements in Hubert space. Liet. Matem. Rink. 31, 50-61 (in Russian).
    • (1991) Liet. Matem. Rink. , vol.31 , pp. 50-61
    • Gudynas, P.1
  • 14
    • 0001131932 scopus 로고
    • On the rate of convergence in the central limit theorem for martingales with discrete and continuous time
    • Haeusler, E. (1988). On the rate of convergence in the central limit theorem for martingales with discrete and continuous time. Ann. Probab. 16, 275-299.
    • (1988) Ann. Probab. , vol.16 , pp. 275-299
    • Haeusler, E.1
  • 16
    • 0000550947 scopus 로고
    • On the departure from normality of a certain class of martingales
    • Heyde, C. C., and Brown, B. M. (1970). On the departure from normality of a certain class of martingales. Ann. Math. Statist. 41, 2161-2165.
    • (1970) Ann. Math. Statist. , vol.41 , pp. 2161-2165
    • Heyde, C.C.1    Brown, B.M.2
  • 17
    • 0002237639 scopus 로고
    • A central limit theorem for a class of dependent random variables
    • Ibragimov, I. A. (1963). A central limit theorem for a class of dependent random variables. Theory Probab. Appl. 8, 83-89.
    • (1963) Theory Probab. Appl. , vol.8 , pp. 83-89
    • Ibragimov, I.A.1
  • 19
    • 34250956889 scopus 로고
    • Eine neue herleitung des exponentialgesetzes in der wahrscheinlichkeitsrechnung
    • Lindeberg, J. W. (1922). Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung. Math. Z. 15, 211-225.
    • (1922) Math. Z. , vol.15 , pp. 211-225
    • Lindeberg, J.W.1
  • 20
    • 0348198070 scopus 로고
    • Results on probabilities of moderate deviations
    • Michel, R. (1974). Results on probabilities of moderate deviations. Ann. Probab. 2, 249-253.
    • (1974) Ann. Probab. , vol.2 , pp. 249-253
    • Michel, R.1
  • 21
    • 33747855434 scopus 로고
    • On the conditional covariance condition in the martingale CLT
    • Račkauskas, A. (1995). On the conditional covariance condition in the martingale CLT. Liet. Matem. Rink. 35, 118-131.
    • (1995) Liet. Matem. Rink. , vol.35 , pp. 118-131
    • Račkauskas, A.1
  • 23
    • 0009990226 scopus 로고
    • Probabilities of moderate deviations
    • Rubin, H., and Sethuraman, J. (1965). Probabilities of moderate deviations. Sankhyā Ser. A 37, 325-346.
    • (1965) Sankhyā Ser. A , vol.37 , pp. 325-346
    • Rubin, H.1    Sethuraman, J.2
  • 25
    • 33747852545 scopus 로고    scopus 로고
    • Moderate deviations for some dependent variables, part I: Martingales
    • Worms, J. (2001). Moderate deviations for some dependent variables, part I: Martingales. Math. Methods Statist. 10, 38-72.
    • (2001) Math. Methods Statist. , vol.10 , pp. 38-72
    • Worms, J.1
  • 26
    • 0011468755 scopus 로고
    • Concerning a certain probability problem
    • Zolotarev, V. M. (1961). Concerning a certain probability problem. Theory frobab. Appl. 6, 201-203.
    • (1961) Theory Frobab. Appl. , vol.6 , pp. 201-203
    • Zolotarev, V.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.