Asymptotic Expected Number of Passages of a Random Walk Through an Interval

Asymptotic Expected Number of Passages of a Random Walk Through an Interval

In this note we find a new result concerning the asymptotic expected number of passages of an finite or infinite interval (x, x + h] as x → ∞ for a random walk with increments having a positive expected value. If the increments are distributed like X, then the limit for 0 < h < ∞ turns out to have the form Emin(|X|, h)/EX which unexpectedly is indpendent of h for the special case where |X| ≤ b ...

Expected Number of Local Maxima of Some Gaussian Random Polnomials

Asymptotic properties of a bold random walk.

In a recent paper we proposed a non-Markovian random walk model with memory of the maximum distance ever reached from the starting point (home). The behavior of the walker is different from the simple symmetric random walk only when she is at this maximum distance, where, having the choice to move either farther or closer, she decides with different probabilities. If the probability of a forwar...

Escape of a Uniform Random Walk from an Interval

We study the first-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the finite range [−a, a]. For a of the order of one, the exit probabilities to each edge of the interval and the exit time from the interval exhibit anomalous properties stemming from the change in the minimum number of steps to escape the interval as a ...

Expected Coverage of Random Walk Mobility Algorithm

Unmanned aerial vehicles (UAVs) have been increasingly used for exploring areas. Many mobility algorithms were designed to achieve a fast coverage of a given area. We focus on analysing the expected coverage of the symmetric random walk algorithm with independent mobility. Therefore we proof the dependence of certain events and develop Markov models, in order to provide an analytical solution f...