A Family of non-Gaussian Martingales with Gaussian Marginals

Details A Family of non-Gaussian Martingales with Gaussian Marginals A Family of non-Gaussian Martingales with Gaussian Marginals

2006-04-06

arxiv.org/abs/math/0604127v1

Mathematics

Probability

16 pages, 2 figures

Scientific paper

We construct a family of non-Gaussian martingales the marginals of which are all Gaussian. We give the predictable quadratic variation of these processes and show they do not have continuous paths. These processes are Markovian and inhomogeneous in time, and we give their infinitesimal generators. Within this family we find a class of piecewise deterministic pure jump processes and describe the laws of jumps and times between the jumps.

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