Sticky-threshold diffusions, local time approximation and parameter estimation

Sara Mazzonetto (1, 2) , Alexis Anagnostakis (3)

1 PASTA - Processus aléatoires spatio-temporels et leurs applications
2 IECL - Institut Élie Cartan de Lorraine
3 LJK - Laboratoire Jean Kuntzmann

We study a class of high frequency path functionals of a diffusion with a sticky-oscillating-skew (SOS) threshold, including the case of a sticky-reflection, and establish convergence to the local time. This extends existing results on sticky, oscillating (regime-switching) and skew or reflecting diffusions in several directions. First, it considers any normalizing sequence that diverges slower than n. Second, it allows combinations of these features. Based on this, and an approximation of the occupation time, we devise consistent skew and stickiness parameter estimators.

Mots clés: stickiness; skewness; reflection; Local time approximation; occupation time statistics; Sticky Brownian motion; Skew Brownian Motion; Oscillating Brownian Motion; Threshold diffusion; oscillating diffusion coefficient

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Sara Mazzonetto, Alexis Anagnostakis. Sticky-threshold diffusions, local time approximation and parameter estimation. 2024. ⟨hal-04503682v1⟩