In this paper, we prove that an isotropic complex symmetric α-stable random measure () can be approximated by a complex process constructed by integrals based on the Poisson process with random intensity.

Let be a d-dimensional bifractional Brownian motion with Hurst parameters and . Assuming , we prove that the renormalized self-intersection local time exists in if and only if , where δ denotes the Dirac delta function. Our work generalizes the result of the renormalized self-intersection local time for fractional Brownian motion.

In this paper, we obtain two approximations in law of the complex fractional Brownian motion by processes constructed from a Poisson process and a Lévy process, respectively. MSC: 60F05; 60G15; 60G22

No abstract