Satunnaiskävelymalliin

Satunnaiskävelymalli, or random walk model, is a mathematical concept describing a path that consists of a succession of random steps. At each step, the direction is chosen randomly. This model has broad applications in various fields.

In physics, random walks are used to model the diffusion of particles in a fluid. Imagine a molecule in water, its movement is influenced by constant collisions with water molecules, leading to a seemingly erratic path. This Brownian motion is a classic example of a random walk.

In finance, the random walk hypothesis suggests that stock prices change randomly and unpredictably. This implies that past price movements cannot be used to predict future price changes, making it difficult to consistently outperform the market.

Computer science utilizes random walks for algorithms such as PageRank, used by Google to rank web pages. It simulates a random surfer clicking on links to determine the importance of a page.

The basic random walk is often defined on a one-dimensional line, where at each step, the walker moves either left or right with equal probability. However, the model can be extended to two or more dimensions, and the probabilities of moving in different directions can be varied. The key characteristic remains the absence of a predetermined direction, with each step being independent of the previous ones.