Unformatted text preview: + b Â± b + 2 p X ( t ) Â² dP ( t ) , where E[ P ( t )] = Î» t and X (0) = x > 0, with probability one, while Î» , a and b are real constants. ( Hint: Find a power transformation to convert the SDE to a constant coeï¬ƒcient SDE. ) 4. For JumpDiï¬€usion SDE, Find Coeï¬ƒcients Transformable to Constant Coeï¬ƒcient SDE. Show that the (ItË† o) jumpdiï¬€usion SDE for X ( t ), dX ( t ) = f ( X ( t )) dt + bX a ( t ) dW ( t ) + h ( X ( t )) dP ( t ) , (3) can be transformed by Y ( t ) = F ( X ( t )) to a constant coeï¬ƒcient SDE , where b and a 6 = 1 are real constants, and X (0) = x > 0, with probability one. In a proper answer, derive the power forms of f ( X ( t )) and h ( X ( t )) from the constant coeï¬ƒcient SDE conditions. Also, what is the answer when a = 1? 1...
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 Fall '09
 Hansen
 Calculus, Probability theory, Stochastic process, Following, constant coeï¬ƒcient sde

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