Invariance principles for local times at the supremum of random walks and Lévy processes

Details Invariance principles for local times at the supremum of random walks and Lévy processes Invariance principles for local times at the supremum of random walks and Lévy processes

2009-03-22

arxiv.org/abs/0903.3705v1

Mathematics

Probability

Scientific paper

We prove that when a sequence of L\'evy processes $X^{(n)}$ or a normed sequence of random walks $S^{(n)}$ converges a.s. on the Skorokhod space toward a L\'evy process $X$, the sequence $L^{(n)}$ of local times at the supremum of $X^{(n)}$ converges uniformly on compact sets in probability toward the local time at the supremum of $X$. A consequence of this result is that the sequence of (quadrivariate) ladder processes (both ascending and descending) converges jointly in law towards the ladder processes of $X$. As an application, we show that in general, the sequence $S^{(n)}$ conditioned to stay positive converges weakly, jointly with its local time at the future minimum, towards the corresponding functional for the limiting process $X$. From this we deduce an invariance principle for the meander which extends known results for the case of attraction to a stable law.

Affiliated with

Also associated with

No associations

Rating

Invariance principles for local times at the supremum of random walks and Lévy processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Invariance principles for local times at the supremum of random walks and Lévy processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invariance principles for local times at the supremum of random walks and Lévy processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-190754