Transcription of LECTURE NOTES ON DONSKER’S THEOREM - Math
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LECTURE NOTES ON DONSKER’S THEOREM - Math
LECTURE NOTES ON donsker S THEOREMDAVAR KHOSHNEVISANABSTRACT. Some course NOTES on donsker s THEOREM . These are forMath 7880-1 ( Topics in Probability ), taught at the Deparment of Math-ematics at the University of Utah during the Spring semester of are constantly being updated and corrected. Read them atyour own authors thanks the National Science Foundation for their continued INTRODUCTIONLet {Xn} n=1denote random variables, all taking values inR. De-fineSn:=X1+ +Xn n the classical central limit THEOREM : THEOREM (CLT).IfE[X1]= andVar(X1) := 2 (0, ), thenSn n pn N(0, 2),where means weak convergence (or convergence in distribution), andN(m,v)denotes the normal distribution with mean m Rand variancev> is a most rudimentary example of an invariance principle.
LECTURE NOTES ON DONSKER’S THEOREM DAVARKHOSHNEVISAN ABSTRACT.Some course notes on Donsker’s theorem. These are for Math7880-1(“TopicsinProbability”),taughtattheDeparmentofMath-
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