Stochasticità

Stochasticità, or stochasticity, refers to the quality of being governed by chance or randomness rather than fixed, deterministic rules. In mathematics and science, stochasticity describes systems in which outcomes are inherently probabilistic, and only statements about likelihoods can be made about future states. This contrasts with deterministic systems, where a given initial condition implies a specific future trajectory.

In probability theory, a stochastic process is a family of random variables indexed by time or space. Stochasticity is often modeled through probability distributions, random shocks, or noise. Common models include Markov chains, which describe memoryless transitions; Brownian motion, modeling continuous random movement; and Gaussian processes, where any finite set of points has a multivariate normal distribution.

Quantifying stochasticity involves estimating distributions, moments such as mean and variance, and other descriptors. Repetition or sampling is used to infer the underlying random behavior. In data analysis, randomness is distinguished from systematic patterns via hypothesis testing, confidence intervals, and model comparison. Stochasticity can also refer to the presence of random effects or unobserved factors in a model.

Applications span finance (random walk of asset prices), physics (particle diffusion), biology (genetic drift, population dynamics), computer science (randomized algorithms, Monte Carlo methods), and engineering (noise in measurements). The concept emphasizes that uncertainty is an intrinsic aspect of many real-world systems and must be addressed explicitly in modeling and inference.