FRACLAB Functions |
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Generates a Mutli-fractional Brownian Motion (mBm) using Wood and Chan circulant matrix, some krigging and a prequantification
MBM = mBmQuantifKrigeage(N,H,K)
MBM = mBmQuantifKrigeage(...,'Propertyname',Propertyvalue)
MBM = mBmQuantifKrigeage(N,H,K) Generates the multi-fractional brownian motion, MBM, using a sample size, N, a Holder function, H,and a number, K, of levels for the prequantification. This allows to model a process the pointwise regularity of which varies in time. The parameter N is a positive integer.
MBM = mBmQuantifKrigeage(...,'Propertyname',Propertyvalue) Generates the multi-fractional brownian motion, MBM, applying the specified property settings. The property setting can be choosen from the list below :
Property | Purpose |
---|---|
'support' |
The MBM is computed using a specific size of time support, TMAX. The parameter TMAX
is a positive integer. |
'sigma' |
The MBM is computed using a specific standard deviation, S, at instant t = 1. |
'seed' |
The MBM is computed with a specific random seed, SEED. This is useful to generate the same path several times or to compare the paths of different MBMs. |
N = 1024; t = linspace(0,1,N); Ht = eval('0.5+0.3*sin(4*pi*t)'); k = 10;
mbm = mBmQuantifKrigeage(N,Ht,k);
figure; plot(t,mbm);
title('Multi-Fractional Brownian Motion with H(t)'); xlabel('time')
N = 2048; t = linspace(0,1,N); Ht = eval('0.1+0.8*t'); k = 10;
mbm1 = mBmQuantifKrigeage(N,Ht,k,'support',1,'seed',100);
mbm2 = mBmQuantifKrigeage(N,Ht,k,'support',5,'seed',100);
figure; plot(mbm1,'k'); hold on; plot(mbm2,'r');
legend('mbm1: Tmax = 1','mbm2: Tmax = 5','Location','NorthWest');
title('Multi-Fractional Brownian Motion with different Tmax');
xlabel('number of points');xlim([0 N])
N = 2048; t = linspace(0,1,N); Ht = eval('0.5+0.3*sin(4*pi*t)');
k1 = 10; k2 = 1;
mbm1 = mBmQuantifKrigeage(N,Ht,k1,'seed',100);
mbm2 = mBmQuantifKrigeage(N,Ht,k2,'seed',100);
figure; plot(mbm1,'k'); hold on; plot(mbm2,'r');
legend('mbm1: K = 10','mbm2: K = 1','Location','NorthWest');
title('Multi-Fractional Brownian Motion with different levels for the prequantification');
xlabel('number of points');xlim([0 N])
mbmlevinson, fbmwoodchan, fbmlevinson
[1] O. Barrière, "Synthèse et estimation de mouvements Browniens multifractionnaires et autres processus à régularité prescrite. Définition du processus autorégulé multifractionnaire et applications", PhD Thesis (2007).
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mbmlevinson | monolr | ![]() |