A more restrictive

random walk model requires independence involving higher conditional moments like the variance, skewness, and kurtosis of the probability distribution of price changes.

Keywords:

Random walk, Market efficiency, Variance ratio, GARCH

If the market is efficient, the model would fail to identify any pattern and it can be inferred that the returns follow a

random walk process.

Price movements in speculative markets: trends or

random walks, Industrial Management Review 2: 7-26.

As another example, in [4]

random walks are used as a tool for sampling complex networks.

A critical aspect is that the time-scale variation indicator can not be described as a

random walk as in Tab.

Asymptotic results concernning the absorption times of

random walks with a barrier.

Four timeseries models are employed as expectation models: account-specific Box-Jenkins ARIMA models, a

random walk, a seasonal

random walk, and a vector autoregressive model.

Researchers have used such

random walks to model a wide range of phenomena, from the diffusion of perfume molecules through still air to the twists and turns of polymer strands.

By the self similarity of the Sierpinski gasket and the Markov property of the

random walks it readily verifies that this time-space-scaling will occur on all magnification scales, and also in the limit approaching continuous time (see also (Lin90)).

We were surprised by the fact that a relatively simple question about

random walks could be so rich," Stanley says.

Iasnogorodski, V Malyshev,

Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications, Springer, 1999.