Before implementing any of the selected tests, the existence of correlations between market returns was studied, as they offer early insights into the markets that do not follow a random walk
. When a market is identified as being weak-form efficient, stock prices follow a random walk
, indicating that price changes are independent and not related to each other, and that historical information is fully and instantaneously reflected in current prices.
Although he did not exploit all richness of his model, Langevin obtained in the long-time regime Einstein's result, namely, by <[x.sup.2]> = 2([k.sub.B]T/6[pi]a[mu])t, where a is the radius of particle, [mu] is fluid viscosity, T is temperature, and [k.sub.B] is the Boltzmann's constant, hence bridging Brownian motion, random walk
, and diffusion, a view soon quantified experimentally by Perrin .
Scher, "Application of continuous time random walk
theory to tracer test measurements in fractured and heterogeneous porous media," Groundwater, vol.
Wendler, "Empirical processes for recurrent and transient random walks
in random scenery," https://arxiv.org/abs/1711.10202.
This modified model gives rise to a random walk
behavior of the electrostatic field that can be analyzed as a Markovian stochastic process.
For this object, we take advantage of random walks
on weighted networks and thus can make use of reversible Markov chains theory.
We compared the movements of Aquilonastra anomala sea stars to three random walk
models (Brownian motion, Levy walks, and correlated random walks
) by examining the sea stars' step length and turn angle distributions.
Semantic relations among words uses two separate random walk
algorithm to estimate candidate confidence.
 was used in EDFC strategy to disseminate source packets among the entire network.
Keywords: random walk
, market efficiency, information, capital markets.
The aim of this paper is to point out observations that the results of a random walk
on G, combined with the results on open book decompositions and closed braids, lead to various interesting and non-trivial properties on random open books and closed braids.
WOESS, Random walks
on infinite graphs and groups, Cambridge Tracts in Mathematics (2000).