메뉴 건너뛰기




Volumn 96, Issue 1-3, 2007, Pages 247-262

An almost-Markov-type mixing condition and large deviations for boolean models on the line

Author keywords

Berry Esseen bound; Cram r type large deviations relations; Higher order covariances; Mixed cumulants; Poisson grain model on the line; Thermodynamic limit; Total length of clumps

Indexed keywords

BOOLEAN ALGEBRA; FUNCTION EVALUATION; MARKOV PROCESSES; POISSON DISTRIBUTION; PROBLEM SOLVING;

EID: 34248584760     PISSN: 01678019     EISSN: 15729036     Source Type: Journal    
DOI: 10.1007/s10440-007-9105-2     Document Type: Conference Paper
Times cited : (5)

References (21)
  • 1
    • 9844260058 scopus 로고    scopus 로고
    • Estimating diffusion coefficients from count data: Einstein-Smoluchowski theory revisited
    • Bingham, N.H., Dunham, B.: Estimating diffusion coefficients from count data: Einstein-Smoluchowski theory revisited. Ann. Inst. Stat. Math. 49, 667-679 (1997)
    • (1997) Ann. Inst. Stat. Math , vol.49 , pp. 667-679
    • Bingham, N.H.1    Dunham, B.2
  • 2
    • 6544263867 scopus 로고    scopus 로고
    • Non-parametric estimation for the M/G/∞ queue
    • Bingham, N.H., Pitts, S.M.: Non-parametric estimation for the M/G/∞ queue. Ann. Inst. Stat. Math. 51, 71-97 (1999)
    • (1999) Ann. Inst. Stat. Math , vol.51 , pp. 71-97
    • Bingham, N.H.1    Pitts, S.M.2
  • 3
    • 0342581623 scopus 로고
    • m-dependent random fields with analytic cumulant generating function
    • Götze, F., Heinrich, L., Hipp, C.: m-dependent random fields with analytic cumulant generating function. Scand. J. Stat. 22, 183-195 (1995)
    • (1995) Scand. J. Stat , vol.22 , pp. 183-195
    • Götze, F.1    Heinrich, L.2    Hipp, C.3
  • 5
    • 0010183950 scopus 로고    scopus 로고
    • Heinrich, L.: A method for the derivation of limit theorems for sums of m-dependent random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 60, 501-515 (1982)
    • Heinrich, L.: A method for the derivation of limit theorems for sums of m-dependent random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 60, 501-515 (1982)
  • 6
    • 0039674729 scopus 로고
    • A method for the derivation of limit theorems for sums of weakly dependent random variables: A survey
    • Heinrich, L.: A method for the derivation of limit theorems for sums of weakly dependent random variables: A survey. Optimization 18, 715-735 (1987)
    • (1987) Optimization , vol.18 , pp. 715-735
    • Heinrich, L.1
  • 7
    • 14544298828 scopus 로고    scopus 로고
    • Large deviations of the empirical volume fraction for stationary Poisson grain models. Ann. Appl. Probab
    • 1A
    • Heinrich, L.: Large deviations of the empirical volume fraction for stationary Poisson grain models. Ann. Appl. Probab. 15(1A), 392-420 (2005)
    • (2005) , vol.15 , pp. 392-420
    • Heinrich, L.1
  • 8
    • 0001446839 scopus 로고
    • Normal convergence of multidimensional shot-noise and rates of this convergence
    • Heinrich, L., Schmidt, V.: Normal convergence of multidimensional shot-noise and rates of this convergence. Adv. Appl. Probab. 17, 709-730 (1985)
    • (1985) Adv. Appl. Probab , vol.17 , pp. 709-730
    • Heinrich, L.1    Schmidt, V.2
  • 9
    • 0345753788 scopus 로고    scopus 로고
    • Kernel estimation of the diameter distribution in Boolean models with spherical grains
    • Heinrich, L., Werner, M. : Kernel estimation of the diameter distribution in Boolean models with spherical grains. J. Nonparam. Stat. 12, 147-176 (2000)
    • (2000) J. Nonparam. Stat , vol.12 , pp. 147-176
    • Heinrich, L.1    Werner, M.2
  • 10
    • 34248511595 scopus 로고    scopus 로고
    • Strongly consistent estimation in Wicksell's corpuscle problem in case of incompletely unobservable spheres in the intersection plane
    • submitted
    • Heinrich, L., Werner, M.: Strongly consistent estimation in Wicksell's corpuscle problem in case of incompletely unobservable spheres in the intersection plane. Ann. Inst. Stat. Math. (2007, submitted)
    • (2007) Ann. Inst. Stat. Math
    • Heinrich, L.1    Werner, M.2
  • 14
    • 0013098425 scopus 로고
    • Some problems in spectral theory of higher order moments I
    • Shiryaev, A.N.: Some problems in spectral theory of higher order moments I. Theory Probab. Appl. 5, 265-284 (1960)
    • (1960) Theory Probab. Appl , vol.5 , pp. 265-284
    • Shiryaev, A.N.1
  • 15
    • 85202320097 scopus 로고    scopus 로고
    • Statulevičius, V.A.: On large deviations. Z. Wahrscheinlichkeitstheorie verw. Gebiete 6, 133-144 (1966)
    • Statulevičius, V.A.: On large deviations. Z. Wahrscheinlichkeitstheorie verw. Gebiete 6, 133-144 (1966)
  • 16
    • 34248567627 scopus 로고    scopus 로고
    • Statulevičius, V.A.: On limit theorems for random functions I. Liet. Mat. Rink. 10, 583-592 (1970) (in Russian)
    • Statulevičius, V.A.: On limit theorems for random functions I. Liet. Mat. Rink. 10, 583-592 (1970) (in Russian)
  • 17
    • 4243971140 scopus 로고
    • Large-deviation theorems for sums of dependent random variables I
    • Statulevičius, V.A.: Large-deviation theorems for sums of dependent random variables I. Lith. Math. J. 19, 289-296 (1979)
    • (1979) Lith. Math. J , vol.19 , pp. 289-296
    • Statulevičius, V.A.1
  • 18
    • 0010797656 scopus 로고
    • On a condition of almost Markov regularity
    • Statulevičius, V.A.: On a condition of almost Markov regularity. Theory Probab. Appl. 28, 379-383 (1983)
    • (1983) Theory Probab. Appl , vol.28 , pp. 379-383
    • Statulevičius, V.A.1
  • 20
    • 0003438596 scopus 로고
    • The Spectral Analysis of Time
    • North-Holland, Amsterdam
    • Žurbenko, I.G.: The Spectral Analysis of Time Series. North-Holland Series in Statistics and Probability, vol. 2. North-Holland, Amsterdam (1986)
    • (1986) Series , vol.2
    • Žurbenko, I.G.1
  • 21
    • 34248553393 scopus 로고    scopus 로고
    • Zuyev, N.M.: An estimate of mixed semiinvariants of random processes satisfying an almost Markov type mixing condition. Liet. Mat. Rink. 21, 81-85 (1981) (in Russian)
    • Zuyev, N.M.: An estimate of mixed semiinvariants of random processes satisfying an almost Markov type mixing condition. Liet. Mat. Rink. 21, 81-85 (1981) (in Russian)


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.