Conclusion
La modélisation d'une économie gouvernée
par les phénomènes aléatoires conduit aux mauvaises
prévisions rendant certainement les politiques économiques
inefficaces.
70
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84
Table des matières
|
1 Préliminaires mathématiques
1.1 Eléments de la théorie de la mesure et
intégration
|
6
6
|
|
1.1.1
|
Limite inférieure et supérieure
|
7
|
|
1.1.2
|
Espaces vectoriels normés
|
8
|
|
1.1.3
|
Propriétés de l'intégrale des fonctions
étagées positives
|
9
|
|
1.1.4
|
Produit des espaces mesurés
|
10
|
|
1.1.5
|
Conditionnement et indépendance de probabilité. . .
.
|
11
|
|
1.2
|
Espérance conditionnelle
|
11
|
|
1.2.1
|
Variables aléatoires
|
13
|
|
1.2.2
|
Modes de convergence
|
13
|
|
1.3
|
Processus stochastiques
|
16
|
|
1.3.1
|
Processus de Markov
|
16
|
|
1.3.2
|
Chaînes de Markov
|
19
|
|
1.3.3
|
Temps d'arrêt
|
21
|
|
1.3.4
|
Martingales à état indépendant
|
22
|
|
1.3.5
|
Mouvement brownien
|
23
|
|
1.3.6
|
Quelques modification du mouvement brownien . . . .
|
24
|
85
1.3.7 Martingales et Semimartingales
|
2 Equations Différentielles et Intégrales
Stochastiques
|
26
31
|
|
2.1
|
Calculs stochastique
|
31
|
|
2.2
|
Equations différentielles stochastiques
|
33
|
|
2.2.1
|
Equations différentielles stochastiques ordinaires . .
|
. . 33
|
|
2.2.2
|
Equations aux dérivées partielles stochastiques
|
34
|
|
2.3
|
Intégrales stochastiques
|
37
|
|
2.3.1
|
Intégrale Stochastique d'Itô
|
37
|
|
2.3.2
|
Intégrale Stochastique de Stratonovich
|
40
|
|
2.4
|
Schémas numériques
|
41
|
|
2.4.1
|
Schéma d'Euler
|
42
|
|
2.4.2
|
Schéma de Milstein
|
43
|
|
2.4.3
|
Schéma de Heun
|
44
|
|
2.4.4
|
Méthodes de Runge - Kutta
|
44
|
|
2.4.5
|
Schéma de Platen
|
45
|
3 Applications des intégrales stochastiques
à l'estimation sta-
tistique 46
3.1 Estimation de paramètres des équations
différentielles stochas-
tiques 46
| 
