Transcription of Stochastic Difierential Equations
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Stochastic Difierential Equations
Bernt ksendalStochastic Differential EquationsAn Introduction with ApplicationsFifth Edition, Corrected PrintingSpringer-Verlag Heidelberg New YorkSpringer-VerlagBerlin Heidelberg NewYorkLondon Paris TokyoHong Kong BarcelonaBudapestTo My FamilyEva, Elise, Anders and Karina2 The front cover shows four sample pathsXt( 1), Xt( 2), Xt( 3) andXt( 4)of a geometric Brownian motionXt( ), of the solution of a (1-dimensional) Stochastic differential equation of the formdXtdt= (r+ Wt)Xtt 0 ;X0=xwherex, rand are constants andWt=Wt( ) is white noise. This process isoften used to model exponential growth under uncertainty . See Chapters 5,10, 11 and figure is a computer simulation for the casex=r= 1, = mean value ofXt,E[Xt] = exp(t), is also drawn.
applications, namely the martingale representation theorem (Chapter IV), the variational inequalities associated to optimal stopping problems (Chapter X) and stochastic control with terminal conditions (Chapter XI). In addition solutions and extra hints to some of the exercises are now included. Moreover,
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