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Volumn 8, Issue 4, 2000, Pages 369-384

Convergence of the Weierstrass-mandelbrot process to fractional Brownian motion

Author keywords

Fractional brownian motion; Functional central limit theorem; Martingale difference sequences; Strong mixing; Weierstrass function; Weierstrass mandelbrot process

Indexed keywords


EID: 0347467583     PISSN: 0218348X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218348X00000408     Document Type: Article
Times cited : (19)

References (14)
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  • 3
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    • Hardy, G.H.1
  • 5
    • 0000955099 scopus 로고
    • On the Weierstrass-Mandelbrot Fractal Function
    • M. V. Berry and Z. V. Lewis "On the Weierstrass-Mandelbrot Fractal Function," Proc. Royal Soc. Lond. A370, 459-484 (1980).
    • (1980) Proc. Royal Soc. Lond. , vol.A370 , pp. 459-484
    • Berry, M.V.1    Lewis, Z.V.2
  • 6
    • 85193381798 scopus 로고    scopus 로고
    • The Weierstrass-Mandelbrot Process Revisited
    • Preprint
    • J. Szulga and F. Molz, The Weierstrass-Mandelbrot Process Revisited. Preprint (1997), to appear in J. Stat. Physics.
    • (1997) J. Stat. Physics
    • Szulga, J.1    Molz, F.2
  • 7
    • 0041571279 scopus 로고
    • Weighted Sums of i.i.d. Random Variables Attracted to Integrals of Stable Processes
    • Y. Kasahara and M. Maejima, "Weighted Sums of i.i.d. Random Variables Attracted to Integrals of Stable Processes," Prob. Th. Rel. Fields 78, 75-96 (1988).
    • (1988) Prob. Th. Rel. Fields , vol.78 , pp. 75-96
    • Kasahara, Y.1    Maejima, M.2
  • 8
    • 0000390031 scopus 로고
    • Basic Properties of Strong Mixing Conditions
    • eds. E. Eberlein and M. S. Taqqu Birkhäuser
    • R. C. Bradley, "Basic Properties of Strong Mixing Conditions," in Dependence in Probability and Statistics, eds. E. Eberlein and M. S. Taqqu (Birkhäuser, 1986), pp. 165-192.
    • (1986) Dependence in Probability and Statistics , pp. 165-192
    • Bradley, R.C.1
  • 9
    • 0242716055 scopus 로고
    • On Martingale Central Limit Theory
    • eds. E. Eberlein and M. S. Taqqu Birkhäuser
    • P. Gaenssler and E. Haeusler, "On Martingale Central Limit Theory, in Dependence in Probability and Statistics, eds. E. Eberlein and M. S. Taqqu (Birkhäuser, 1986), pp. 303-334.
    • (1986) Dependence in Probability and Statistics , pp. 303-334
    • Gaenssler, P.1    Haeusler, E.2
  • 10
    • 85193350523 scopus 로고    scopus 로고
    • Convergence of Weighted Sums of Random Variables with Long-Range Dependence
    • Preprint
    • V. Pipiras and M. S. Taqqu, Convergence of Weighted Sums of Random Variables with Long-Range Dependence. Preprint (1999), to appear in Stochastics Proc. Appl.
    • (1999) Stochastics Proc. Appl.
    • Pipiras, V.1    Taqqu, M.S.2
  • 11
    • 85037470970 scopus 로고    scopus 로고
    • The Weierstass-Mandelbrot Process Provides a Series Approximation to the Harmonizable Fractional Stable Motion
    • eds. C. Bandt, S. Graf and M. Zähle Birkhäuser
    • V. Pipiras and M. S. Taqqu, "The Weierstass-Mandelbrot Process Provides a Series Approximation to the Harmonizable Fractional Stable Motion," in Fractal Geometry and Stochastics II, eds. C. Bandt, S. Graf and M. Zähle (Birkhäuser, 2000), pp. 161-179.
    • (2000) Fractal Geometry and Stochastics II , pp. 161-179
    • Pipiras, V.1    Taqqu, M.S.2
  • 14
    • 0002720637 scopus 로고
    • Recent Advances in the Central Limit Theorem and Its Weak Invariance Principle for Mixing Sequences of Random Variables
    • eds. E. Eberlein and M. S. Taqqu Birkhäuser
    • M. Peligrad, "Recent Advances in the Central Limit Theorem and Its Weak Invariance Principle for Mixing Sequences of Random Variables," in Dependence in Probability and Statistics, eds. E. Eberlein and M. S. Taqqu (Birkhäuser, 1986), pp. 193-224.
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    • Peligrad, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.