sztochasztikus

Sztochasztikus is a Hungarian adjective meaning related to stochastic processes or randomness in mathematics, statistics, and related fields. It describes systems or models influenced by chance rather than fully deterministic rules. The term denotes a framework in which uncertainty is modeled using probability laws and random variables, rather than fixed outcomes.

A central concept is the stochastic process, a collection of random variables indexed by time or another parameter, representing the evolution of a system under uncertainty. Related notions include random variables, probability distributions, independence, and stationarity. Stochastic models can be classified as discrete-time or continuous-time; common examples are random walks, Poisson processes, and Brownian motion. Analytical tools include expectation, variance, conditioning, filtrations, and, for continuous-time models, stochastic calculus such as Itô calculus, used to formulate and solve stochastic differential equations.

Sztochasztikus models appear across disciplines. In finance, they underlie asset pricing and risk management (for example, models for stock prices and interest rates). In physics and engineering, they describe diffusion and noise-driven dynamics. In biology and epidemiology, stochastic models capture random variability in populations and disease spread. Queueing theory and telecommunications also rely on stochastic methods to analyze performance under randomness.

History and terminology: the English term stochastic derives from Greek stochastikos, related to chance or guesswork, and its Hungarian counterpart sztochasztikus follows the same lineage. The concept gained formal grounding in the 20th century through contributions by Kolmogorov, Wiener, Ito, and others, shaping modern probability theory and its applications.