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Does there exist a martingale which has Marginal distributions same as Brownian Motion marginals but the process itself not being Brownian motion? Any references are highly appreciated. Thanks.

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  • $\begingroup$ What exactly do you mean by marginals? Marginals at a single time? At finitely many times? $\endgroup$ – Daniel McLaury Dec 19 '13 at 9:48
  • $\begingroup$ Marginal distribution at any time t should be Gaussian with zero mean and variance t. $\endgroup$ – chandu1729 Dec 19 '13 at 10:14
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This looks relevant.

Kais Hamza and Fima C. Klebaner, “A Family of Non-Gaussian Martingales with Gaussian Marginals,” Journal of Applied Mathematics and Stochastic Analysis, vol. 2007, Article ID 92723, 19 pages, 2007. doi:10.1155/2007/92723

http://www.hindawi.com/journals/ijsa/2007/092723/abs/

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