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$$dW_3 = \rho \, dW_1(t) + \sqrt{1- \rho^2} \ dW_2(t) $$

I tried applying Levy theorem. My question is should the Levy theorem argument be used for which part of the above equation?

Michael Hardy
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kateBay1
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    The mean is right, the variance is right, the whole thing is clearly Gaussian. Check the covariance. – Ian Jul 14 '16 at 03:02
  • @Ian :How do you calculate the mean and variance? –  Jul 14 '16 at 03:11
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    The process will be just $\rho W_1 + \sqrt{1-\rho^2} W_2$. For each time $t$, this is a sum of two independent Gaussian r.v.s with mean zero, one with variance $\rho^2 t$, the other with variance $(1-\rho^2)t$. The variances add up to $t$, which is what it should be. Now get the time covariance basically the same way. – Ian Jul 14 '16 at 04:59

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