257 lines
17 KiB
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257 lines
17 KiB
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\providecommand\hyper@newdestlabel[2]{}
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\citation{dodge2004statistique}
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\citation{dodge2004statistique}
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\@writefile{lof}{\addvspace {10pt}}
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\@writefile{toc}{\contentsline {appendix}{\chapternumberline {A}\IeC {\'E}l\IeC {\'e}ments de th\IeC {\'e}orie des probabilit\IeC {\'e}s}{115}{appendix.A}}
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\@writefile{toc}{\contentsline {section}{\numberline {A.1}D\IeC {\'e}finitions de base}{115}{section.A.1}}
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\newlabel{sec:introvariablealeatoire}{{A.1}{115}{Définitions de base}{section.A.1}{}}
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\citation{stuart1987kendall}
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\newlabel{eq:repartitiondefinition}{{A.1.5}{116}{Définitions de base}{equation.A.1.0.5}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {A.2}Transform\IeC {\'e}es d'une variable al\IeC {\'e}atoire}{116}{section.A.2}}
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\newlabel{sec:transformees}{{A.2}{116}{Transformées d'une variable aléatoire}{section.A.2}{}}
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\@writefile{toc}{\contentsline {subsubsection}{Transform\IeC {\'e}e de Fourier}{116}{section*.53}}
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\newlabel{sec:transfourier}{{A.2.1}{116}{Transformée de Fourier}{section*.53}{}}
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\newlabel{sec:transfourier@cref}{{[subsubappendix][1][2147483647,1,2]A.2.1}{116}}
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\@writefile{toc}{\contentsline {subsubsection}{D\IeC {\'e}finition}{116}{section*.54}}
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\newlabel{sec:deffncaract}{{A.2.1}{116}{Définition}{section*.54}{}}
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\newlabel{sec:deffncaract@cref}{{[subsubappendix][1][2147483647,1,2]A.2.1}{116}}
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\newlabel{eq:deffncaract}{{A.2.3}{116}{Définition}{equation.A.2.0.3}{}}
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\newlabel{eq:deffncaract@cref}{{[equation][3][2147483647,1,2]A.2.3}{116}}
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\citation{lukacs1960characteristic}
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\citation{gil1951note}
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\citation{epps2007pricing}
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\citation{wendel1961non}
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\@writefile{toc}{\contentsline {subsubsection}{Les moments}{117}{section*.55}}
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\newlabel{sec:momentsfncaract}{{A.2.1}{117}{Les moments}{section*.55}{}}
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\newlabel{sec:momentsfncaract@cref}{{[subsubappendix][1][2147483647,1,2]A.2.1}{117}}
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\newlabel{eq:defmoments}{{A.2.4}{117}{Les moments}{equation.A.2.0.4}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A.2.2}Inversion de la fonction caract\IeC {\'e}ristique}{117}{subsection.A.2.2}}
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\@writefile{toc}{\contentsline {subsubsection}{La densit\IeC {\'e}}{117}{section*.56}}
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\newlabel{sec:densitefncaract}{{A.2.2}{117}{La densité}{section*.56}{}}
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\newlabel{sec:densitefncaract@cref}{{[subsubappendix][2][2147483647,1,2]A.2.2}{117}}
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\newlabel{eq:caractdensite}{{A.2.6}{117}{La densité}{equation.A.2.0.6}{}}
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\@writefile{toc}{\contentsline {subsubsection}{La fonction de r\IeC {\'e}partition}{117}{section*.57}}
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\newlabel{sec:repartitionfncaract}{{A.2.2}{117}{La fonction de répartition}{section*.57}{}}
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\newlabel{sec:repartitionfncaract@cref}{{[subsubappendix][2][2147483647,1,2]A.2.2}{117}}
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\newlabel{eq:gilpelaez}{{A.2.7}{117}{La fonction de répartition}{equation.A.2.0.7}{}}
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\newlabel{eq:gilpelaez@cref}{{[equation][7][2147483647,1,2]A.2.7}{117}}
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\newlabel{eq:gilpelaez2}{{A.2.8}{117}{La fonction de répartition}{equation.A.2.0.8}{}}
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\newlabel{eq:gilpelaez2@cref}{{[equation][8][2147483647,1,2]A.2.8}{117}}
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\citation{shephard1991characteristic}
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\newlabel{eq:inversionfncaract}{{A.2.9}{118}{La fonction de répartition}{equation.A.2.0.9}{}}
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\newlabel{eq:inversionfncaract@cref}{{[equation][9][2147483647,1,2]A.2.9}{118}}
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\newlabel{eq:shepherd}{{A.2.10}{118}{La fonction de répartition}{equation.A.2.0.10}{}}
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\newlabel{eq:shepherd@cref}{{[equation][10][2147483647,1,2]A.2.10}{118}}
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\newlabel{eq:approxinvfncaract}{{A.2.11}{118}{La fonction de répartition}{equation.A.2.0.11}{}}
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\newlabel{eq:approxinvfncaract@cref}{{[equation][11][2147483647,1,2]A.2.11}{118}}
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\newlabel{eq:convocaract}{{A.2.12}{118}{La fonction de répartition}{equation.A.2.0.12}{}}
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\newlabel{eq:convocaract@cref}{{[equation][12][2147483647,1,2]A.2.12}{118}}
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\newlabel{eq:convocaractIID}{{A.2.13}{118}{La fonction de répartition}{equation.A.2.0.13}{}}
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\newlabel{eq:convocaractIID@cref}{{[equation][13][2147483647,1,2]A.2.13}{118}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A.2.3}La fonction g\IeC {\'e}n\IeC {\'e}ratrice des moments}{118}{subsection.A.2.3}}
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\newlabel{sec:fgm}{{A.2.3}{118}{La fonction génératrice des moments}{subsection.A.2.3}{}}
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\newlabel{sec:fgm@cref}{{[subsubappendix][3][2147483647,1,2]A.2.3}{118}}
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\newlabel{eq:deffngenmom}{{A.2.14}{118}{La fonction génératrice des moments}{equation.A.2.0.14}{}}
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\newlabel{eq:deffngenmom@cref}{{[equation][14][2147483647,1,2]A.2.14}{118}}
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\citation{stuart1987kendall}
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\newlabel{eq:fgmmoments}{{A.2.15}{119}{La fonction génératrice des moments}{equation.A.2.0.15}{}}
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\newlabel{eq:fgmmoments@cref}{{[equation][15][2147483647,1,2]A.2.15}{119}}
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\newlabel{eq:fncaractfgm}{{A.2.16}{119}{La fonction génératrice des moments}{equation.A.2.0.16}{}}
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\newlabel{eq:fncaractfgm@cref}{{[equation][16][2147483647,1,2]A.2.16}{119}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A.2.4}La fonction g\IeC {\'e}n\IeC {\'e}ratrice des cumulants}{119}{subsection.A.2.4}}
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\newlabel{sec:fgc}{{A.2.4}{119}{La fonction génératrice des cumulants}{subsection.A.2.4}{}}
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\newlabel{sec:fgc@cref}{{[subsubappendix][4][2147483647,1,2]A.2.4}{119}}
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\newlabel{eq:fgc}{{A.2.17}{119}{La fonction génératrice des cumulants}{equation.A.2.0.17}{}}
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\newlabel{eq:fgc@cref}{{[equation][17][2147483647,1,2]A.2.17}{119}}
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\newlabel{eq:cumulantsempiriques}{{A.2.18}{119}{La fonction génératrice des cumulants}{equation.A.2.0.18.18}{}}
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\newlabel{eq:cumulantsempiriques@cref}{{[equation][18][2147483647,1,2]A.2.18}{119}}
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\newlabel{eq:cumulantsempiriques1}{{A.2.18a}{119}{La fonction génératrice des cumulants}{equation.A.2.0.18a}{}}
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\newlabel{eq:cumulantsempiriques1@cref}{{[equation][1][2147483647,1,2,18]A.2.18a}{119}}
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\newlabel{eq:cumulantsempiriques2}{{A.2.18b}{119}{La fonction génératrice des cumulants}{equation.A.2.0.18b}{}}
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\newlabel{eq:cumulantsempiriques2@cref}{{[equation][2][2147483647,1,2,18]A.2.18b}{119}}
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\newlabel{eq:cumulantsempiriques3}{{A.2.18c}{119}{La fonction génératrice des cumulants}{equation.A.2.0.18c}{}}
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\newlabel{eq:cumulantsempiriques3@cref}{{[equation][3][2147483647,1,2,18]A.2.18c}{119}}
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\newlabel{eq:cumulantsempiriques4}{{A.2.18d}{119}{La fonction génératrice des cumulants}{equation.A.2.0.18d}{}}
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\newlabel{eq:cumulantsempiriques4@cref}{{[equation][4][2147483647,1,2,18]A.2.18d}{119}}
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\newlabel{eq:derivfgc}{{A.2.19}{119}{La fonction génératrice des cumulants}{equation.A.2.0.19}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A.2.5}La transform\IeC {\'e}e d'Esscher}{120}{subsection.A.2.5}}
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\newlabel{sec:transesscher}{{A.2.5}{120}{La transformée d'Esscher}{subsection.A.2.5}{}}
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\newlabel{sec:transesscher@cref}{{[subsubappendix][5][2147483647,1,2]A.2.5}{120}}
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\newlabel{eq:esschertransform}{{A.2.20}{120}{La transformée d'Esscher}{equation.A.2.0.20}{}}
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\newlabel{eq:esschertransform@cref}{{[equation][20][2147483647,1,2]A.2.20}{120}}
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\newlabel{eq:esscherMx}{{A.2.21}{120}{La transformée d'Esscher}{equation.A.2.0.21}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {A.3}La transform\IeC {\'e}e de Fourier rapide}{120}{section.A.3}}
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\newlabel{sec:methodeFFT}{{A.3}{120}{La transformée de Fourier rapide}{section.A.3}{}}
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\newlabel{sec:methodeFFT@cref}{{[subappendix][3][2147483647,1]A.3}{120}}
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\newlabel{eq:sommefft}{{A.3.1}{120}{La transformée de Fourier rapide}{equation.A.3.0.1}{}}
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\newlabel{eq:sommefft@cref}{{[equation][1][2147483647,1,3]A.3.1}{120}}
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\newlabel{eq:sommeifft@cref}{{[equation][2][2147483647,1,3]A.3.2}{120}}
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\citation{barndorff2001levy}
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\newlabel{eq:sommefftdensite}{{A.3.3}{121}{La transformée de Fourier rapide}{equation.A.3.0.3.3}{}}
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\newlabel{eq:sommefftdensite@cref}{{[equation][3][2147483647,1,3]A.3.3}{121}}
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\newlabel{eq:sommefftdensite1}{{A.3.3a}{121}{La transformée de Fourier rapide}{equation.A.3.0.3a}{}}
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\newlabel{eq:sommefftdensite2}{{A.3.3b}{121}{La transformée de Fourier rapide}{equation.A.3.0.3b}{}}
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\newlabel{eq:signalfftfonction@cref}{{[equation][4][2147483647,1,3]A.3.4}{121}}
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\newlabel{eq:fftfonction}{{A.3.5}{121}{La transformée de Fourier rapide}{equation.A.3.0.5}{}}
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\newlabel{eq:fftfonction@cref}{{[equation][5][2147483647,1,3]A.3.5}{121}}
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\newlabel{eq:densitefftfonction}{{A.3.6}{121}{La transformée de Fourier rapide}{equation.A.3.0.6}{}}
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\newlabel{eq:densitefftfonction@cref}{{[equation][6][2147483647,1,3]A.3.6}{121}}
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\@writefile{toc}{\contentsline {section}{\numberline {A.4}Processus de L\IeC {\'e}vy}{121}{section.A.4}}
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\newlabel{sec:processuslevy}{{A.4}{121}{Processus de Lévy}{section.A.4}{}}
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\newlabel{sec:processuslevy@cref}{{[subappendix][4][2147483647,1]A.4}{121}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A.4.1}D\IeC {\'e}finition et propri\IeC {\'e}t\IeC {\'e}s}{121}{subsection.A.4.1}}
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\newlabel{sec:defproplevy}{{A.4.1}{121}{Définition et propriétés}{subsection.A.4.1}{}}
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\newlabel{sec:defproplevy@cref}{{[subsubappendix][1][2147483647,1,4]A.4.1}{121}}
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\citation{applebaum2004levy}
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\@writefile{toc}{\contentsline {subsubsection}{Repr\IeC {\'e}sentation de L\IeC {\'e}vy-Khintchine}{122}{section*.58}}
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\newlabel{sec:levykhintchine}{{A.4.1}{122}{Représentation de Lévy-Khintchine}{section*.58}{}}
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\newlabel{sec:levykhintchine@cref}{{[subsubappendix][1][2147483647,1,4]A.4.1}{122}}
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\newlabel{eq:levykhintchine}{{A.4.1}{122}{Représentation de Lévy-Khintchine}{equation.A.4.0.1}{}}
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\@writefile{toc}{\contentsline {subsubsection}{Repr\IeC {\'e}sentation de L\IeC {\'e}vy-It\IeC {\^o}}{122}{section*.59}}
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\newlabel{sec:levyito}{{A.4.1}{122}{Représentation de Lévy-Itô}{section*.59}{}}
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\newlabel{sec:levyito@cref}{{[subsubappendix][1][2147483647,1,4]A.4.1}{122}}
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\newlabel{eq:levyitodecomposition}{{A.4.3}{122}{Représentation de Lévy-Itô}{equation.A.4.0.3}{}}
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\newlabel{eq:levyitodecomposition@cref}{{[equation][3][2147483647,1,4]A.4.3}{122}}
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\citation{sato1999levy}
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\citation{schoutens2003levy}
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\citation{kyprianou2007introductory}
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\citation{teschl2004topics}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A.4.2}Processus subordonn\IeC {\'e}}{123}{subsection.A.4.2}}
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\newlabel{sec:procsubordonne}{{A.4.2}{123}{Processus subordonné}{subsection.A.4.2}{}}
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\newlabel{sec:procsubordonne@cref}{{[subsubappendix][2][2147483647,1,4]A.4.2}{123}}
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\newlabel{eq:exposantcaractYt@cref}{{[equation][6][2147483647,1,4]A.4.6}{123}}
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\newlabel{eq:fncaractYt}{{A.4.7}{123}{Processus subordonné}{equation.A.4.0.7}{}}
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\newlabel{eq:fncaractYt@cref}{{[equation][7][2147483647,1,4]A.4.7}{123}}
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\newlabel{eq:densiteprocessusyt}{{A.4.8}{123}{Processus subordonné}{equation.A.4.0.8}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {A.5}Th\IeC {\'e}or\IeC {\`e}mes d'int\IeC {\'e}gration}{123}{section.A.5}}
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