stokastilise

Stokastiline (stokastilise) is an Estonian adjective referring to stochastic, i.e., involving randomness. In mathematics and applied disciplines, stokastiline models describe systems whose future state is not determined solely by the present state but also by random factors. The term is used across statistics, probability theory, physics, finance, engineering, and computer science.

In probability theory, a stochastic process is a family of random variables indexed by time, X_t. Such models are built on a probability space (Ω, F, P). They can be discrete-time, like a random walk, or continuous-time, like Brownian motion. Many stokastiline models use the Markov property (memorylessness), though non-Markov models are common as well. Key concepts include randomness sources, distributions, expectation, variance, and correlation. Measured properties are often described in terms of probability distributions or sample paths. Stokastiline modeling enables estimation, forecasting, and risk assessment under uncertainty.

Applications include finance (stock prices modeled as stochastic processes; Black-Scholes model, Monte Carlo pricing), queueing theory (service systems), physics (diffusion), biology (population dynamics), and engineering (stochastic reliability). Analytical solutions are sometimes possible, but many problems require numerical simulation or stochastic calculus. Monte Carlo methods simulate many realizations to approximate distributions; stochastic differential equations model continuous-time dynamics and are analyzed with Itô calculus.

In summary, stokastilise models acknowledge randomness as an intrinsic part of system behavior, providing probabilistic predictions and uncertainty quantification rather than deterministic forecasts. See also probability theory, stochastic process, stochastic differential equation.