The tag has no wiki summary.

learn more… | top users | synonyms

20
votes
5answers
2k views

A random walk with uniformly distributed steps

The following problem has bothered me for a long time. Let us imagine a point on the real axis. At the beginning, it is located at point $O$. Then it will "walk" on the real axis randomly in the ...
11
votes
3answers
400 views

An “inchworm-like” random walk on an integer interval

Imagine I place $k$ stones on an infinite one-dimensional integer interval $Z$ s.t. no stone is more than some distance $d$ from any other stone. For example, if $d=1$ and $k = 5$, we might place the ...
5
votes
1answer
173 views

Random walk with positive uniformly distributed steps

Let $U_1,U_2,\ldots$ be iid random variables distributed uniformly on $[0,1]$. I am interested in the random walk $X_i = \sum_{j \leq i} U_j$. In particular, What is the expected number of points ...
4
votes
1answer
195 views

Approximating a hitting time for some state using the stationary distribution?

Provided a random walk on a bounded interval, with step probabilities, $p$ and $q$ and a stationary distribution $\pi$, how "bad" of an approximation is to assume that the hitting time for a position ...
3
votes
1answer
278 views

Where does directed random walk hit the boundary of a region?

I have a problem that I more or less know the answer to (in an ad hoc way), but would really like to see it done in a systematic way. In spite of this, I will pose the question in quite a concrete ...
1
vote
1answer
469 views

Hitting time probability in a Random Walk with possibility to die.

A Random Walker can move of one unit to the right with probability $p$, to the left with probability $q$ and it can jump again to the starting point with probability $r$ and die. Naturally $p+q+r=1$. ...