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DynamicalTheories
of
BrownianMotion
secondedition
by
EdwardNelson
DepartmentofMathematics
PrincetonUniversity
Contents
1.Apology....................................................1
2.RobertBrown...............................................5
3.TheperiodbeforeEinstein..................................9
4.AlbertEinstein.............................................13
5.DerivationoftheWienerprocess............................19
6.Gaussianprocesses..........................................27
7.TheWienerintegral.........................................31
8.Aclassofstochasticdi?erentialequations...................37
9.TheOrnstein-UhlenbecktheoryofBrownianmotion.........45
10.Brownianmotioninaforce?eld.............................53
11.Kinematicsofstochasticmotion.............................65
12.Dynamicsofstochasticmotion..............................83
13.KinematicsofMarkovianmotion............................85
14.Remarksonquantummechanics............................89
15.Brownianmotionintheaether..............................105
16.Comparisonwithquantummechanics.......................111
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