# hmw2 - dX t = aX t dt + bX t dW t ; where a < and b >...

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Numerical Methods for SDEs, Fall 2006. Course Instructor: Ra´ul Tempone. Homework Set 2, due Thursday Sept 14. Last revised, Aug 26, 2006. Exercise 1 a Consider the ordinary diﬀerential equation dX t = AX t dt where X t R 2 and the matrix A has two real eigenvalues λ 1 = 1 and λ 2 = - 10 5 . Then the backward Euler method X ( t n +1 ) - X ( t n ) = AX ( t n +1 )( t n +1 - t n ) is an eﬃcient method to solve the problem (why?). b Formulate and motivate a backward Euler method for approximation of the Ito SDE
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Unformatted text preview: dX t = aX t dt + bX t dW t ; where a < and b > are constants. Exercise 2 Solve the exercise 3.17 from the lecture notes [GMS + 06] References [GMS + 06] J. Goodman, K.S. Moon, A. Szepessy, R. Tempone, and Z. Zouraris. Stochastic and Partial Diﬀerential 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.

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