Persistence exponent for random processes in Brownian scenery
Résumé
We consider the one-sided exit problem for random processes in Brownian scenery, that is the asymptotic behaviour for large $T$, of the probability $$\mathbb{P}\Big[ \sup_{t\in[0,T]} \Delta_t \leq 1\Big] $$ where $$\Delta_t = \int_{\mathbb{R}} L_t(x) \, dW(x).$$ Here $W=\{W(x); x\in\mathbb{R}\}$ is a two-sided standard real Brownian motion and $\{L_t(x); x\in\mathbb{R},t\geq 0\}$ is the local time of some self-similar random process with stationary increments, independent from the process $W$.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)