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Stochastic Calculus, Filtering, and Stochastic Control

StochasticCalculus, Filtering, andStochast icControlLecture Notes(Thisversion:May29,2007)RamonvanHan delSpring2007 PrefaceTheselecturenoteswerewrittenforth ecourseACM217:AdvancedTopicsin Stochas-ticAnalysisat Caltech;thisyear(2007), anintroductorycourseonthesubject,andasth ereareonlysomany weeksina term, suf cientdodevelopa largeclassofinterestingmodels,andto developsomestochasticcontroland ,andmany otherfascinating(anduseful)topics,arelef tfora , thestochasticcontrolportionofthesenotesc oncentratesonveri- cationtheorems, hope,however, thattheinterestedreaderwillbeencouragedt oprobea littledeeperandultimatelytomove have noillusionsaboutthestateofthesenotes they werewrittenratherquickly,sometimesatther ateofa chaptera have nodoubtthatmany errorsremaininthetext;at theveryleastmany oftheproofsareextremelycompact,andshould bemadea littleclearerasis be ttingofa pedagogical(?)

Introduction This course is about stochastic calculus and some of its applications. As the name suggests, stochastic calculus provides a mathematical foundation for the treatment of equations that involve noise. The various problems which we will be dealing with,

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