We consider a d-parameter Hermite process with Hurst index H=(H 1 ,.,H d )∈1/2,1 d and we study its limit behavior in distribution when the Hurst parameters H i ,i=1,.,d (or a part of them) converge to 1/2 and/or 1. The limit obtained is Gaussian (when at least one parameter tends to 1/2) and non-Gaussian (when at least one-parameter tends to 1 and none converges to 1/2).
- Fractional Brownian motion
- Hermite process
- Multiparameter stochastic processes
- Multiple stochastic integrals
- Rosenblatt process
- Wiener chaos