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.

  • $\begingroup$ 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

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



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.