\relax 
\catcode`:\active
\catcode`;\active
\catcode`!\active
\catcode`?\active
\select@language{french}
\@writefile{toc}{\select@language{french}}
\@writefile{lof}{\select@language{french}}
\@writefile{lot}{\select@language{french}}
\@writefile{toc}{\contentsline {chapter}{Introduction}{4}}
\@writefile{toc}{\contentsline {chapter}{Remerciements}{7}}
\@writefile{toc}{\contentsline {chapter}{\numberline {1}Variables aléatoires}{9}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{pta}{{1.1}{10}}
\newlabel{ptb}{{1.2}{11}}
\newlabel{holder}{{1.3}{11}}
\newlabel{holder_1}{{1.4}{11}}
\newlabel{holder_2}{{1.5}{11}}
\newlabel{ptc}{{1.6}{12}}
\newlabel{minkowsky}{{1.7}{12}}
\newlabel{jensen}{{1.8}{12}}
\newlabel{ptd}{{1.9}{13}}
\@writefile{toc}{\contentsline {chapter}{\numberline {2}Algèbres de variables aléatoires}{15}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{lof}{\contentsline {figure}{\numberline {2.1}{\ignorespaces lancer de dés}}{17}}
\newlabel{fig_2_1}{{2.1}{17}}
\@writefile{toc}{\contentsline {chapter}{\numberline {3}Processus stochastiques}{21}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{moyenne}{{3.1}{22}}
\@writefile{toc}{\contentsline {chapter}{\numberline {4}Concepts externes}{25}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\citation{reeb}
\@writefile{lof}{\contentsline {figure}{\numberline {4.1}{\ignorespaces les entiers naturels}}{29}}
\newlabel{fig_4_1}{{4.1}{29}}
\@writefile{toc}{\contentsline {chapter}{\numberline {5}Infinitésimaux}{31}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\citation{reeb}
\@writefile{toc}{\contentsline {chapter}{\numberline {6}Analogues externes de notions internes}{37}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{lof}{\contentsline {figure}{\numberline {6.1}{\ignorespaces la quasi-convergence}}{39}}
\newlabel{fig_6_1}{{6.1}{39}}
\@writefile{lof}{\contentsline {figure}{\numberline {6.2}{\ignorespaces encore la quasi-convergence}}{39}}
\newlabel{fig_6_2}{{6.2}{39}}
\citation{reeb}
\@writefile{toc}{\contentsline {chapter}{\numberline {7}Propriétés vraies presque partout}{45}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{eq_71}{{7.1}{47}}
\newlabel{eq_72}{{7.2}{48}}
\@writefile{toc}{\contentsline {chapter}{\numberline {8}Variables aléatoires ${L^1}$}{53}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {chapter}{\numberline {9}Décomposition des processus stochastiques}{59}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{eq_91}{{9.1}{60}}
\newlabel{eq_93}{{9.3}{63}}
\@writefile{toc}{\contentsline {chapter}{\numberline {10}Variation totale d'un processus}{65}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {chapter}{\numberline {11}Convergence des martingales}{71}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{eq_11_1}{{11.1}{72}}
\newlabel{eq_11_2}{{11.2}{72}}
\newlabel{eq_11_3}{{11.3}{72}}
\@writefile{lof}{\contentsline {figure}{\numberline {11.1}{\ignorespaces deux stratégies d'investissement}}{73}}
\newlabel{fig_11_1}{{11.1}{73}}
\newlabel{eq_11_4}{{11.4}{73}}
\@writefile{lof}{\contentsline {figure}{\numberline {11.2}{\ignorespaces une mauvaise martingale}}{76}}
\newlabel{fig_11_2}{{11.2}{76}}
\@writefile{toc}{\contentsline {chapter}{\numberline {12}Fluctuations des martingales}{81}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{lof}{\contentsline {figure}{\numberline {12.1}{\ignorespaces deux trajectoires}}{82}}
\newlabel{fig_12_1}{{12.1}{82}}
\@writefile{lof}{\contentsline {figure}{\numberline {12.2}{\ignorespaces discontinuités}}{82}}
\newlabel{fig_12_2}{{12.2}{82}}
\newlabel{eq_12_1}{{12.1}{84}}
\@writefile{lof}{\contentsline {figure}{\numberline {12.3}{\ignorespaces franchissements de ${\left [\lambda _1,\lambda _2\right ]}$}}{84}}
\newlabel{fig_12_3}{{12.3}{84}}
\newlabel{eq_12_2}{{12.2}{85}}
\newlabel{eq_12_3}{{12.3}{85}}
\@writefile{toc}{\contentsline {chapter}{\numberline {13}Discontinuités des martingales}{87}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{lof}{\contentsline {figure}{\numberline {13.1}{\ignorespaces une autre stratégie d'investissement}}{89}}
\newlabel{fig_13_1}{{13.1}{89}}
\newlabel{eq_13_1}{{13.1}{89}}
\@writefile{toc}{\contentsline {chapter}{\numberline {14}La condition de Lindeberg}{93}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{eq_14_1}{{14.1}{93}}
\newlabel{eq_14_2}{{14.2}{94}}
\@writefile{lof}{\contentsline {figure}{\numberline {14.1}{\ignorespaces variation quadratique}}{96}}
\newlabel{fig_14_1}{{14.1}{96}}
\@writefile{toc}{\contentsline {chapter}{\numberline {15}Maximum des martingales}{99}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{eq_15_1}{{15.1}{99}}
\newlabel{eq_15_2}{{15.2}{100}}
\@writefile{toc}{\contentsline {chapter}{\numberline {16}La loi des grands nombres}{103}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{eq_16_1}{{16.1}{103}}
\newlabel{eq_16_2}{{16.2}{104}}
\@writefile{toc}{\contentsline {chapter}{\numberline {17}Processus quasiment équivalents}{115}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{eq_17_1}{{17.1}{119}}
\@writefile{toc}{\contentsline {chapter}{\numberline {18}Théorème de de~Moivre-Laplace-Lindeberg-Feller-Wiener-Lévy-Doob-Erd\H os-Kac-Donsker-Prokhorov}{121}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{lof}{\contentsline {figure}{\numberline {18.1}{\ignorespaces un processus de Wiener}}{124}}
\newlabel{fig_18_1}{{18.1}{124}}
\newlabel{eq_18_1}{{18.1}{126}}
\newlabel{eq_18_2}{{18.2}{126}}
\newlabel{eq_18_3}{{18.3}{127}}
\citation{nelson_1}
\citation{reeb}
\citation{nelson_2}
\@writefile{toc}{\contentsline {chapter}{Annexe}{129}}
\newlabel{eq_A_1}{{1}{130}}
\newlabel{eq_A_2}{{2}{130}}
\newlabel{eq_A_3}{{3}{133}}
\newlabel{eq_A_4}{{4}{134}}
\newlabel{eq_A_5}{{5}{134}}
\newlabel{eq_A_6}{{6}{134}}
\newlabel{eq_A_7}{{7}{135}}
\citation{nelson_3}
\newlabel{eq_A_8}{{8}{137}}
\newlabel{eq_A_9}{{9}{137}}
\newlabel{eq_A_10}{{10}{138}}
\newlabel{eq_A_11}{{11}{138}}
\bibcite{nelson_1}{1}
\bibcite{nelson_trad}{2}
\bibcite{nelson_2}{3}
\bibcite{nelson_3}{4}
\bibcite{reeb}{5}
\bibcite{cnrs}{6}
\bibcite{lobry}{7}
\bibcite{salanskis}{8}
\bibcite{billingsley}{9}
\@writefile{toc}{\contentsline {chapter}{Bibliographie}{145}}
\@writefile{toc}{\contentsline {chapter}{Index}{147}}
\@writefile{toc}{\contentsline {chapter}{Table des figures}{150}}