\contentsline {section}{\numberline {1}Avertissement}{2}
\contentsline {section}{\numberline {2}Introduction}{2}
\contentsline {subsection}{\numberline {2.1}G\'en\'eration de nombres pseudo--al\'eatoires}{2}
\contentsline {subsection}{\numberline {2.2}M\'ethodes num\'eriques probabilistes}{2}
\contentsline {section}{\numberline {3}Variables al\'eatoires}{2}
\contentsline {subsection}{\numberline {3.1}Loi uniforme}{3}
\contentsline {paragraph}{Applet : Densit\'e empirique d'un \'echantillon d'une loi uniforme $U[0,1]$}{3}
\contentsline {paragraph}{Applet : Pile ou face}{3}
\contentsline {paragraph}{Applet : loi uniforme sur le carr\'e unit\'e}{3}
\contentsline {subsection}{\numberline {3.2}Loi normale}{3}
\contentsline {paragraph}{Applet : La planche de Galton}{3}
\contentsline {subsection}{\numberline {3.3}Algorithmes}{4}
\contentsline {subsubsection}{\numberline {3.3.1}Deux m\'ethodes pour calculer $\pi $}{4}
\contentsline {paragraph}{Applet : L'Aiguille de Buffon}{4}
\contentsline {paragraph}{Applet : Calcul de $\pi $ par m\'ethode de Monte--Carlo}{4}
\contentsline {subsubsection}{\numberline {3.3.2}Recuit simul\'e}{4}
\contentsline {paragraph}{Applet : Recuit simul\'e}{5}
\contentsline {paragraph}{Applet : Probl\`eme du voyageur de commerce}{5}
\contentsline {section}{\numberline {4}Processus stochastiques}{5}
\contentsline {subsection}{\numberline {4.1}Marche al\'eatoire}{5}
\contentsline {paragraph}{Applet : marche au hasard}{6}
\contentsline {subsection}{\numberline {4.2}Mouvement brownien}{6}
\contentsline {subsubsection}{\numberline {4.2.1}D\'efinition}{6}
\contentsline {subsubsection}{\numberline {4.2.2}Approximation}{6}
\contentsline {paragraph}{Applet : Mouvement brownien dans le carr\'e unit\'e}{7}
\contentsline {paragraph}{Applet : Mouvement brownien, aspect fractal}{7}
\contentsline {subsection}{\numberline {4.3}Processus d'Ornstein-Uhlenbeck}{7}
\contentsline {paragraph}{Applet : processus d'Ornstein-Uhlenbeck 2D}{7}
\contentsline {section}{\numberline {5}Quelques liens}{7}
\contentsline {section}{\numberline {6}Cr\'edits}{8}