# Correlate bivariate Brownian bridges

Given two independently constructed Brownian bridges (from their marginal means and variances), is there a way to correlate the sample paths?

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hmm can we consider bridges that are pinned to non-zero locations? Also are the bridges pinned at the same time $t$? If it is as you have linked, where they are constrained to (1,0), then simply: $$cBB^1_t = BB^1_t$$ and $$cBB^2_t = \rho BB^1_t + \sqrt{ 1- \rho^2 }BB^2_t$$ should work. –  Cam.Davidson.Pilon Aug 15 '12 at 14:52
Thanks. So in general to construct the multivariate Brownian bridge from the one-dimensional (based on each marginal), one just need to multiply them by the square root of the variance-covariance matrix? –  Tim Aug 15 '12 at 15:23
Yup, that should do it. –  Cam.Davidson.Pilon Aug 15 '12 at 18:23