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...Stochastic calculus hws david promel universitat mannheim october abstract this is a preliminary version of the lecture notes for course cal culus which will be continuously updated during semester and may contain many mistakes please careful when using it let me know if you nd or have suggestions improvements present are written jointly with mathias trabs karlsruher institut fur technologie contents introduction brownian motion local martingales ito integration construction integral extension via localization formula processes s dierential equations linear sdes lipschitz continuous coecients martingale representation theorem time changes levy characterization girsanov application bachelier model mathematical foundation conditional expectation filtration stopping times backward gronwall lemma radon nikodym b miscellaneous dictionary english german abbreviations recommended literature kuo h to springer steele j m financial applications karatzas i shreve e protter p revuz d yor oksendal ...