Stochastisk

Stochastisk is the term used in Norwegian and Swedish to describe phenomena, models, or variables that involve randomness. In English, the equivalent term is stochastic. The central idea is that outcomes cannot be predicted with certainty, even if a complete statistical description is available. A stochastic model uses random variables to represent uncertain quantities and often describes how these quantities evolve over time or across situations.

A key concept is the stochastic process, a family of random variables indexed by time or another parameter. Examples include Brownian motion (a continuous-time process with continuous paths), Poisson processes (random counts over time), and Markov chains (memoryless random processes). In continuous-time models, stochastic differential equations describe dynamics with both deterministic and random components, typically driven by Brownian motion or other noise sources.

Stochastic models are widely used across disciplines. In finance, they underpin asset price dynamics and risk assessment; in physics, they model diffusion and particle transport; in engineering and operations research, they appear in queueing and reliability analyses; in biology and epidemiology, they capture random effects in populations and disease spread.

The term emphasizes randomness and uncertainty rather than determinism. Stochastic models describe distributions of possible outcomes and their statistical properties (mean, variance, correlations) rather than unique, fixed results. They complement deterministic models by accounting for inherent variability and noise in real-world systems.