Parisian quasi-stationary distributions for asymmetric Lévy processes

In recent years there has been some focus on quasi-stationary behaviour of an one-dimensional Lévy process $X$, where we ask for the law $P(X_t\in dy | τ^-_0>t)$ for $t\to\infty$ and $τ_0^-=\inf\{t\geq 0: X_t<0\}$. In this paper we address the same question for so-called Parisian ruin time $τ^θ$, that happens when process stays below zero longer than independent exponential random variable with intensity $θ$.

No reviews yet.

No comments yet.