Stochastic process is also known as a random process. It is a collection of random variables that represent the evolution of some system of random values over time.
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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.
Stochastic testing is the same as "monkey testing", but stochastic testing is a lot more technical sounding name for the same testing process. Stochastic testing is black box testing, random testing, performed by automated testing tools. Stochastic testing is a series of random tests over time. The software under test typically passes the individual tests, but our goal is to see if it can pass a large number of individual tests.
monte carlo simulation is used to give solutions of deterministic problems whereas stochastic simulation is used for stochastic problems.
Buying a lottery ticket daily is deterministic. Winning a lottery and getting a prize is Stochastic.
the output will be different everyime