w2 (t) be two independent Brownian Motions, that is, for each value of t, w1 , w2 are independent random variables. Then w1 (0) = w2 (0) = 0, E(w1 ) = E(w2 ) = 0 and
2 2 E(w1 ) = E(w2 ) = t
E(w1 w2 ) = E(w2 w1 ) = 0 Let W = Then WWT =
2 w1 w1 w2 2 w2 w1 w2 2 E(w1 ) E(w1 w2 ) 2 E(w2 w1 ) E(w2 )
w1 w2
E(W W T ) = =
1 0 t = It 0 1
Now let z1 (t), z2 (t) be two (possibly) correlated Brownian Motions, that is, for each value of t,
2 2 E(z1 ) = E(z2 ) = t
E(z1 z2 ) = E(z2 z1 ) = ρ12…
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