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Unformatted text preview: Exercise 3 a Solve Exercise 4.10 from [GMS + 06]. b Optional for extra credit. Consider the SDE dX ( t ) =-aX ( t ) dt + b ( X ( t )) dW ( t ) , where a &gt; . Is it possible to determine the function b such that X has a prescribed limit distribution with density p ( x ) as t ? If the answer is yes, carry out explicit computations for the uniform case p ( x ) = 1 , if-. 5 x . 5 , , otherwise. References [GMS + 06] J. Goodman, K.S. Moon, A. Szepessy, R. Tempone, and Z. Zouraris. Stochastic and Partial Dierential Equations with Adapted Numerics. Lecture Notes , 2006. 1...
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This note was uploaded on 12/14/2011 for the course MAD 5932 taught by Professor Gallivan during the Fall '06 term at FSU.
- Fall '06