You can thank Kac and Nelson for the association of stochastic phenomena with probability and probabilistic events. There's a good Wikipedia page explaining in better detail.
Oh, dude, it's like asking the difference between a taco and a burrito - they're both delicious, but they have their own unique flavors. Stochastic is more about randomness and unpredictability, while probabilistic is all about calculating probabilities and likelihoods. So, like, stochastic is the wild card at the party, and probabilistic is the one crunching numbers in the corner.
Yu-Kweng Michael Lin has written: 'Probabilistic theory of structural dynamics' -- subject(s): Stochastic processes, Structural dynamics
Wikipedia states that stochastic means random. But there are differences depending on the context. Stochastic is used as an adjective, as in stochastic process, stochastic model, or stochastic simulation, with the meaning that phenomena as analyzed has an element of uncertainty or chance (random element). If a system is not stochastic, it is deterministic. I may consider a phenomena is a random process and analyze it using a stochastic simulation model. When we generate numbers using a probability distribution, these are called random numbers, or pseudo random numbers. They can also be called random deviates. See related links.
A stochastic error indicates an error that is random between measurements. Stochastics typically occur through the sum of many random errors.
A Stochastic error term is a term that is added to a regression equation to introduce all of the variation in Y that cannot be explained by the included Xs. It is, in effect, a symbol of the econometrician's ignorance or inability to model all the movements of the dependent variable.
The definition to the term "Stochastic Process" is: A statistical process involving a number of random variables depending on a number variable. Which in most cases, is time.
A stochastic disturbance term is a random variable included in a statistical model to account for unexplained variability or uncertainty in the data. It represents the effects of unobserved factors that are not explicitly modeled but can influence the outcome of an analysis. By incorporating this term, the model can better capture the randomness or unpredictability in the data.
The term mutator function is a computer processing term. It is a function that takes a current state and returns a neighbor state, typically in a probabilistic manner.
Stochastic Models was created in 1985.
G. Adomian has written: 'Stochastic systems' -- subject(s): Stochastic differential equations, Stochastic systems
Regression analysis is based on the assumption that the dependent variable is distributed according some function of the independent variables together with independent identically distributed random errors. If the error terms were not stochastic then some of the properties of the regression analysis are not valid.
C. W. Gardiner has written: 'Handbook of Stochastic Methods' 'Stochastic methods' -- subject(s): Stochastic processes 'Quantum noise' -- subject(s): Stochastic processes, Quantum optics, Josephson junctions