Weak convergence of random walks conditioned to stay away

Details Weak convergence of random walks conditioned to stay away Weak convergence of random walks conditioned to stay away

2010-09-03

arxiv.org/abs/1009.0700v1

Mathematics

Probability

6 pages

Scientific paper

Let $\{X_n\}_{n\in\mathbb{N}}$ be a sequence of i.i.d. random variables in $\mathbb{Z}^d$. Let $S_k=X_1+...+X_k$ and $Y_n(t)$ be the continuous process on $[0,1]$ for which $Y_n(k/n)=S_k/\sqrt{n}$ $k=1,...,n$ and which is linearly interpolated elsewhere. The paper gives a generalization of results of Belkin, \cite{B72} on the weak limit laws of $Y_n(t)$ conditioned to stay away from some small sets. In particular, it is shown that the diffusive limit of the random walk meander on $\mathbb Z^d: d\ge 2$ is the Brownian motion.

Affiliated with

Also associated with

No associations

Rating

Weak convergence of random walks conditioned to stay away 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 Weak convergence of random walks conditioned to stay away, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak convergence of random walks conditioned to stay away will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-685130