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Unformatted text preview: formula when necessary. b Assume now that | a ( x )-a ( y ) | C a | x-y | 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 dierent number of time steps: N = 10 , 20 , 40 . 1...
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- Fall '06