lez 1_ processi stocastici
lez 1_ processi stocastici
lez 1_ processi stocastici
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Esempio<br />
Random Walk<br />
discrete-time, discrete-state<br />
Xt X t<br />
= 1 t=1,2,3,...<br />
+ t<br />
where t = {1,1} and<br />
p( t<br />
= 1)<br />
= p(<br />
t<br />
= + 1) = 0,5<br />
3<br />
2<br />
1<br />
0<br />
-1<br />
-2<br />
-3<br />
-4<br />
-5<br />
-6<br />
-7<br />
-8<br />
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16<br />
E. Messina Metodi Computazionali<br />
9<br />
Esempio<br />
Changing p>0,5<br />
we obtain a random walk with drift<br />
12<br />
10<br />
p=0,8<br />
8<br />
6<br />
4<br />
2<br />
0<br />
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18<br />
Another way to generalize this process is to let <br />
(discrete time continuous state stochastic process)<br />
t<br />
assume continuous values<br />
t<br />
N(0,1)<br />
5<br />
4<br />
3<br />
2<br />
1<br />
E. Messina<br />
0<br />
-1<br />
-2<br />
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18<br />
Metodi Computazionali<br />
1<br />
0
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