Unformatted text preview: formula when necessary. b Assume now that  a ( x )a ( y )  ≤ C a  xy  with a positive constant C a . Find bounds for the expectation E (  e ( t )  2 ) use it to bound the variance var ( e ( t )) . Discuss what happens as b → . c Implement a uniform time step forward Euler discretization of the above equations taking a ( x ) = cos( x ) , b = 0 . 1 and T = 6 . Plot the sample estimator for var ( e ( t )) vs. time, and compare it with the bound obtained in part (b). Use M = 10 3 sample paths and diﬀerent number of time steps: N = 10 , 20 , 40 . 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
 gallivan

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