Prove the existence and uniqueness of a1

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Reference no: EM132364425

Assignment Task :

If the Langevin equation is given as

(dy_k)/dt=∑__l A_kl y_l+ζ_k , (k,l=1,2,3) (A1)

Where A_kl is a 3 by 3 constant matrix functionsuch that

?ζ_k (t) ?=0,

?ζ_k (t) ζ_k(t^') ?=B_klδ(t-t' ) (A2)

B_kl is a 3 by 3 constant matrix function.

Show that (A1) is

-iωy ¯_k (ω)=∑_l A_kl y ¯_l (ω)+ζ ¯_k (ω)

and (A2) is

?ζ ¯_k (ω) ζ ¯_l (ω' ) ?=B_kl (2π)δ(ω+ω' )

Find the spectral density of y ¯_k (ω).

Prove the existence and uniqueness of (A1)

NB: Please complete mathematical steps and solutions are required.

Reference no: EM132364425

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