lez 1_ processi stocastici
lez 1_ processi stocastici
lez 1_ processi stocastici
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Stepping Stone Model<br />
Let A be a nxn array of squares<br />
Each square is initially any one of k different colors<br />
For each step, a square is chosen at random<br />
This square chooses one of its 8 neighbors at random and assumes its color<br />
(boundary conditions …)<br />
This is an example of absorbing Markov Chain: with probability 1 all the squares<br />
will eventually all be the same color<br />
Credit Rating: Typical Transition Matrix (1-Year)<br />
Initial<br />
Rating<br />
Year-End Rating<br />
AAA AA A BBB BB B CCC D<br />
AAA 90.81 8.33 0.68 0.06 0.12 0 0 0<br />
AA 0.70 90.65 7.79 0.64 0.06 0.14 0.02 0<br />
A 0.09 2.27 91.05 5.52 0.74 0.26 0.01 0.06<br />
BBB 0.02 0.33 5.95 86.93 5.30 1.17 0.12 0.18<br />
BB 0.03 0.14 0.67 7.73 80.53 8.84 1.00 1.06<br />
B 0 0.11 0.24 0.43 6.48 83.46 4.07 5.20<br />
CCC 0.22 0 0.22 1.30 2.38 11.24 64.86 19.79
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