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.TH "mbmlevinson" 2 " June 6th 1997" "Fractales Group" "Scilab Function"
.so ../sci.an
.SH NAME
mbmlevinson - Levinson synthesis of a multifractional Brownian motion
.sp
Author: Paulo Goncalves
.sp
Generates a Multi-Fractional Brownian Motion (mBm) using Cholesky/Levinson factorization
.sp
.sp
.SH Usage
.sp
.ft CR
.nf
[x,y,r] = mbmlevinson(N,H,[seed])
.fi
.ec
.ft P
.sp
.SH Input parameters
.RS
.TP
o
\fB N \fP : Positive integer
Sample size of the fBm
.TP
o
\fB H \fP : Real vector \f(CR[\fP1,N\f(CR]\fP of character string
\fIH\fP real vector: contains the Holder exponents at each time. Each
element in \f(CR[\fP0,1\f(CR]\fP.
\fIH\fP character string: analytic expression of the Holder function
(e.g. 'abs(0.5 * ( 1 + sin(16 t) ) )')
.TP
o
\fB seed \fP : real scalar
Random seed generator
.RE
.SH Output parameters
.RS
.TP
o
\fB x \fP : real vector \f(CR[\fP1,N\f(CR]\fP
Time samples of the mBm
.TP
o
\fB y \fP : real vector \f(CR[\fP1,N\f(CR]\fP
Vector of N i.i.d. white standard Gaussian r.v.'s (input process of
the generator)
.TP
o
\fB r \fP : real matrix \f(CR[\fPN,N\f(CR]\fP
Matrix containing columnwise each first row of the
var/cov Toeplitz matrices R(n) of the non-stationary
increment process w\f(CR[\fPn\f(CR]\fP = x\f(CR[\fPn+1\f(CR]\fP - x\f(CR[\fPn\f(CR]\fP.
.RE
.SH Algorithm details
For each time \fIn\fP, a fbm process with constant Holder exponent
H\f(CR[\fPn/\f(CR]\fP is synthesized over N points (see
\fIfbmlevinson\fP). Only the sample at rank \fIn\fP is kept. As a
result of this computationally expensive procedure, only small sample
sizes of mBms can be generated (typically less than 1024 samples).
.SH See also:
mbmlevinson
.SH Example:
.sp
.ft CR
.nf
[x,y,r] = mbmlevinson(512,AtanH(512,2,1,0.5)) ;
plot(x) ;
.fi
.ec
.ft P
.sp
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