Condition for intersection occupation measure to be absolutely continuous

UDC 519.21 Given the i.i.d. -valued stochastic processes with the stationary increments, a minimal condition is provided for the occupation measure to be absolutely continuous with respect to the Lebesgue measure on An isometry identity related to the resulting density (known as intersection local time) is also established.

Particle picture representation of the non-symmetric Rosenblatt process and Hermite processes of any order

We provide a particle picture representation for the non-symmetric Rosenblatt process and for Hermite processes of any order, extending the result of Bojdecki, Gorostiza and Talarczyk in [4]. We show that these processes can be obtained as limits of certain functionals of a system of particles evolving according to symmetric stable Lévy motions. In the case of [Formula: see text]-Hermite processes the corresponding functional involves [Formula: see text]-intersection local time of symmetric stable Lévy processes.