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Stochastic Difierential Equations - Main Concepts

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.

The main corrections and improvements in this corrected printing are from ... the close contact between the theoretical achievements and the applications in this area is striking. For example, today very few flrms (if ... In the introduction we state 6 …

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