Estocástica

Estocástica is a term derived from the Greek word stokhos, meaning aim or guess. In mathematics and statistics, it refers to processes or phenomena that involve randomness or uncertainty. A stochastic process is a collection of random variables indexed by time or space, describing the evolution of some random system. This means that at any given point in time, the outcome of the process is not predetermined but has a probability distribution associated with it. Examples of stochastic phenomena include the random walk of a molecule, the fluctuations in stock prices, or the spread of a disease.

The study of stochastic processes is crucial in many scientific fields. It allows researchers to model and understand systems where chance plays a significant role. Key concepts within stochastic processes include probability distributions, random variables, and the expected value. Differentiating between deterministic and stochastic systems is fundamental. A deterministic system's future state can be precisely predicted if its initial state is known, whereas a stochastic system's future state can only be described in terms of probabilities. Mathematical tools like Markov chains and Brownian motion are used to analyze and predict the behavior of stochastic systems.