kappa=10; theta=1; sigma=0.25; % parametre procesu x0=0.5 % zaciatocna hodnota dt=0.001; % casovy krok n=1000; % pocet krokov % Eulerova schema x(1)=x0; for i=1:n dw=sqrt(dt)*randn; dx=kappa*(theta-x(i))*dt+sigma*dw; x(i+1)=x(i)+dx; end; t=0:dt:n*dt; % cas plot(t,x)
Zdroj: (Episcopos, 1998)![]()
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Kijoši Itó (1915 - 2008), zakladateľ teórie stochastických diferenciálnych rovníc.
Životopis na stránke Inamori Foundation Životopis na "The MacTutor History of Mathematics archive" "Dr. Kiyoshi Ito receives the Gauss Prize" |
In precisely built mathematical structures, mathematicians find the same sort of beauty others find in enchanting pieces of music, or in magnificent architecture. There is, however, one great difference between the beauty of mathematical structures and that of great art. Music by Mozart, for instance, impresses greatly even those who do not know musical theory; the cathedral in Cologne overwhelms spectators even if they know nothing about Christianity. The beauty in mathematical structures, however, cannot be appreciated without understanding of a group of numerical formulae that express laws of logic. Only mathematicians can read "musical scores" containing many numerical formulae, and play that "music" in their hearts. Accordingly, I once believed that without numerical formulae, I could never communicate the sweet melody played in my heart. Stochastic differential equations, called "Ito Formula," are currently in wide use for describing phenomena of random fluctuations over time. When I first set forth stochastic differential equations, however, my paper did not attract attention. It was over ten years after my paper that other mathematicians began reading my "musical scores" and playing my "music" with their "instruments."
K. Ito, My Sixty Years in Studies of Probability Theory : acceptance speech of the Kyoto Prize in Basic Sciences (1998). |