A Family of non-Gaussian Martingales with Gaussian Marginals

2006/04/06 by Kaïs Hamza, Hamza, kais, Fima C. Klebaner +1 · 1 citation
Economics, Econometrics and Finance · #60G44 #60J25 #60J75 #91B70 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.math/0604127

openalex publication_date 2006/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• On the Weak Error for Local Stochastic Volatility Models

Related

• Martingale Nature and Laws of the Iterated Logarithm for Markov Processes of Pure-Jump Type
• Partially Gaussian Stationary Stochastic Processes in Discrete Time
• Conic Martingales from Stochastic Integrals
• q-Bass martingales
• Weak Dirichlet processes and generalized martingale problems