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math.PR2018
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…
math.PR2018
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…