6 citations · 8 across the 4 of their papers we have counts for
5 papers
On the distribution of cumulative Parisian ruin
Hélène Guérin, Jean-François Renaud
We introduce the concept of cumulative Parisian ruin, which is based on the time spent in the red by the underlying surplus process. Our main result is an explicit representation f…
Long time behavior of telegraph processes under convex potentials
Joaquin Fontbona, Hélène Guérin, Florent Malrieu
We study the long-time behavior of variants of the telegraph process with position-dependent jump-rates, which result in a monotone gradient-like drift toward the origin. We comput…
Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view
Hélène Guérin, Jean-François Renaud
For a spectrally negative Lévy process , we study the following distribution: $$ \mathbb{E}_x \left[ \mathrm{e}^{- q \int_0^t \mathbf{1}_{(a,b)} (X_s) \mathrm{d}s } ; X_t \in \m…
Quantitative estimates for the long time behavior of an ergodic variant of the telegraph process
Joaquin Fontbona, Hélène Guérin, Florent Malrieu
Motivated by stability questions on piecewise deterministic Markov models of bacterial chemotaxis, we study the long time behavior of a variant of the classic telegraph process hav…
Estimates for the density of a nonlinear Landau process
Hélène Guérin, Sylvie Méléard, Eulalia Nualart
The aim of this paper is to obtain estimates for the density of the law of a specific nonlinear diffusion process at any positive bounded time. This process is issued from kinetic…