4 papers · 1 filter
From Hawkes-type processes to stochastic volatility
Łukasz Treszczotko
We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Th…
Random walks in doubly random scenery
Łukasz Treszczotko
We provide a random walk in random scenery representation of a new class of stable self-similar processes with stationary increments introduced recently by Jung, Owada and Samorodn…
Infinite variance -sssi processes as limits of particle systems
Łukasz Treszczotko
We consider a particle system with weights and the scaling limits derived from its occupation time. We let the particles perform independent recurrent Lévy motions and we assume th…
Particle picture representation of the non-symmetric Rosenblatt process and Hermite processes of any order
Łukasz Treszczotko
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 Talarc…