stohastiline

Stohastiline (stochastic) is an adjective used to describe systems, models, or processes that involve randomness and probability. The term comes from Greek and is used across mathematics, statistics, and applied sciences to distinguish random, inherently uncertain behavior from deterministic descriptions.

In mathematics, a stochastic process is a family of random variables indexed by time that describes how a system evolves under uncertainty. Important classes include discrete-time processes (such as random walks and Markov chains) and continuous-time processes (such as Brownian motion and Poisson processes). The Markov property, stationarity, and independence are common notions used to analyze these processes. Stochastic calculus, including Itô calculus, provides tools for modeling and analyzing continuous-time processes driven by random fluctuations, typically via stochastic differential equations.

Applications of stochastic modeling are wide-ranging. In finance, stochastic models underpin asset prices, risk assessment, and option pricing. In physics and chemistry, they describe diffusion and reaction kinetics; in biology, they model population dynamics and gene frequencies. In engineering and signal processing, stochastic noise and randomness are incorporated into design and analysis. Computer science uses randomized algorithms and Monte Carlo methods, while operations research employs stochastic models for queues, inventory, and optimization under uncertainty.

Common modeling approaches include Monte Carlo simulation, stochastic differential equations, and stochastic optimization. Parameter estimation and model validation rely on statistical inference, often via maximum likelihood or Bayesian methods, using observed data to calibrate the random components of the model.