CONVERGENCE OF THE WEIERSTRASS-MANDELBROT PROCESS TO FRACTIONAL BROWNIAN MOTION

DOI10.1142/S0218348X00000408zbMath0976.60042MaRDI QIDQ2709706

Vladas Pipiras, Murad S. Taqqu

Publication date: 10 December 2001

Published in: Fractals (Search for Journal in Brave)

zbMATH Keywords

functional central limit theoremfractional Brownian motionWeierstrass functionmartingale differencesstrong mixingWeierstrass-Mandelbrot process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Self-similar stochastic processes (60G18) Functional limit theorems; invariance principles (60F17)

Related Items (9)

Hausdorff dimension of Weierstrass-Mandelbrot process ⋮ Convergence of weighted sums of random variables with long-range dependence. ⋮ Control of Weierstrass–Mandelbrot Function Model with Morlet Wavelets ⋮ On the chirp decomposition of Weierstrass-Mandelbrot functions, and their time-frequency interpretation. ⋮ Fractal Haar system ⋮ Filtered Brownian motions as weak limit of filtered Poisson processes ⋮ Wavelets, generalized white noise and fractional integration: The synthesis of fractional Brownian motion ⋮ Stochastic modeling of unresolved scales in complex systems ⋮ Sharp estimates for the covering numbers of the Weierstrass fractal kernel

Cites Work

• Weighted sums of i.i.d. random variables attracted to integrals of stable processes
• On the Weierstrass-Mandelbrot fractal function

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