Stochastic Definition: What Does ‘Stochastic’ Mean?

“Stochastic” is a description that refers to outcomes based upon random probability. Its etymology traces to a Greek word, “stókhos,” meaning "guess." Stochastic systems, stochastic analysis, and stochastic optimization can take place whenever a collection of random variables come into play. Stochastic variables appear in branches of mathematics, computer science, physics, gene expression, cryptography, social science, and information theory. Stochastic algorithms, probability theory, random number generation, and other types of stochastic processes even turn up in the world of music and visual art, as creators use them as novel ways to produce original works.

A stochastic process is an abstract mathematical concept that hinges upon random variables. The Bernoulli process is one such mathematical sequence based on a sequence of independent, identically distributed random variables. Stochastic processes can also factor into higher levels of probabilistic mathematics, such as stochastic calculus which incorporates stochastic differential equations based on the Brownian Motion Process (also called the Wiener Process).

The theory of stochastic processes also underpins Markov Chains (also called the Markov Process), named for the Russian mathematician Andrey Markov who took an interest in independent random sequences. For instance, a Markov Chain Monte Carlo (MCMC) is a class of stochastic algorithms that use probability distributions to simulate random objects. A Markov Chain Monte Carlo can be represented in a stochastic matrix.

Stochastic modeling is a financial planning tool that predicts investment outcomes under randomly selected conditions. This lets financial analysts offer forecasts that are not tainted by their own gut instincts or oversimplified by deterministic modeling, which forecasts based on a fixed, unchanging prediction of future market events.

The Monte Carlo stochastic model, which has its roots in advanced mathematics, also applies to stochastic financial modeling. It predicts financial performance using probability distributions of individual returns on the assets in a particular investment portfolio.

The opposite of a stochastic variable is a deterministic variable.

• Stochastic variables involve randomness. Anything labeled "stochastic" has its roots in random probability. While stochastic modeling can quickly become dense and complicated, it does account for the random chance that often affects real-world outcomes.
• Deterministic variables involve consistency. A deterministic variable or deterministic model assumes the same outcomes will occur every time for a specific set of inputs. It does not account for the random chance that sometimes upends predicted outcomes. Deterministic modeling is simpler and easier to grasp than stochastic modeling, but it only yields reliable predictions in closed environments with fixed parameters and minimum risk of random disruptions and divergence.

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