Abstract
In the present chapter we shall consider the problem of modelling complex-valued fractional Brownian motion of order n (C-(fBm) n in the following).
Statistics is the first of the inexact sciences.
Edmond and Jules de Goncourt
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
COX, D.R.; Long-range dependence, non-linearity and time irreversibility, J. Time Series Analysis, Vol 12, No 4, pp 329–335, 1991
HOCHBERG, G.; Signed measure of probability, Ann. of Probability, Vol 6, No 3, pp 433–458, 1978
JUMARIE, G.; A new approach to complex-valued fractional Brownian motion via rotating white noise, Chaos, Solitons and Fractals, Vol 9, No 6, pp 881–893, 1998
JUMARIE, G.; A new approach to fractional Brownian motion of order n via random walk in the complex plane, Chaos, Solitons and Fractals, Vol 10, No 7, pp 1193–1212, 1999
JUMARIE, G.; Complex-valued measures. An approach via random walk in the complex plane, Statistics and Probab. Letters, Vol 42, No 1, pp 61–67, 1999
LEVY, P.; Stochastic Processes and Brownian Motion (in French), Gauthier Villars, Paris, 1965
MANDELBROT, B.B.; and van NESS J.W.; Fractional Brownian motion, fractional noises and applications, SIAM Rev., Vol 10, No 4, pp 422–437, 1968
MANDELBROT, B.B.; The Fractal Geometry of Nature, W,H, Freeman, New York, 1982; reprint, Plenum Publishing, New York, 1992
SAINTY, P.; Construction of a complex valued fractional Brownian motion of order N, J. Math. Phys., Vol 33, No 9, pp 3128–3149, 1992
ZOLOTAREV, Y.; Transactions of Mathematical Monographs, Vol 65, Amer. Mathematical Society, Providence, 1986
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Jumarie, G. (2000). Complex-Valued Fractional Brownian Motion of Order n. Part I. In: Maximum Entropy, Information Without Probability and Complex Fractals. Fundamental Theories of Physics, vol 112. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9496-7_6
Download citation
DOI: https://doi.org/10.1007/978-94-015-9496-7_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5467-8
Online ISBN: 978-94-015-9496-7
eBook Packages: Springer Book Archive