wfbm and identity function

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jamie
jamie 2014-9-12
编辑： jamie 2014-9-12
Hi,
I am looking at the wfbm documentation and could use some help. It seems the parameter L creates a point for each value of the x-axis. However I want to create a large fbm path only in the region [0,1].
Somewhat like the code I have pasted below would create, any help would be fantastic!
So really I would like to generate the fbrm increments and then multiply them by the identity matrix so (in mathematical notation) it would give me B(x)_H*I(x)_[0,1].
--------------------------------------------------
clear all % generates one dimensional fractional Brownian motion 'W' on t in [0,1] using 'n' grid points % the method used applies FFT to a circulant covariance matrix % for a detailed mathematical explanation of the Matlab code and further % examples see
% Kroese, D.P. and Botev, Z.I. (2013). % "Spatial Process Generation." % V. Schmidt (Ed.). Lectures on Stochastic Geometry, % Spatial Statistics and Random Fields, Volume II: % Analysis, Modeling and Simulation of Complex Structures, Springer-Verlag, Berlin. % weblink: % http://www.maths.uq.edu.au/~kroese/ps/MCSpatial.pdf
hold on n=2^8; % grid points H = 0.75; % Hurst parameter r=nan(n+1,1); r(1) = 1; for k=1:n r(k+1) = 0.5*((k+1)^(2*H) - 2*k^(2*H) + (k-1)^(2*H)); end r=[r; r(end-1:-1:2)]; % first rwo of circulant matrix lambda=real(fft(r))/(2*n); % eigenvalues W=fft(sqrt(lambda).*complex(randn(2*n,1),randn(2*n,1))); W = n^(-H)*cumsum(real(W(1:n+1))); % rescale plot((0:n)/n,W); -------------------------------------------------

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