Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156481 | Stochastic Processes and their Applications | 2014 | 22 Pages |
Abstract
We calculate the density function of (Uâ(t),θâ(t)), where Uâ(t) is the maximum over [0,g(t)] of a reflected Brownian motion U, where g(t) stands for the last zero of U before t, θâ(t)=fâ(t)âgâ(t), fâ(t) is the hitting time of the level Uâ(t), and gâ(t) is the left-hand point of the interval straddling fâ(t). We also calculate explicitly the marginal density functions of Uâ(t) and θâ(t). Let Unâ and θnâ be the analogs of Uâ(t) and θâ(t) respectively where the underlying process (Un) is the Lindley process, i.e. the difference between a centered real random walk and its minimum. We prove that (Unân,θnân) converges weakly to (Uâ(1),θâ(1)) as nââ.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Claudie Chabriac, Agnès Lagnoux, Sabine Mercier, Pierre Vallois,