Stochastic is a term that refers to processes that involve randomness or uncertainty. In other words, a stochastic process is one in which the outcome is not completely determined and is subject to some degree of randomness.

There are many different examples of stochastic processes in various fields, including mathematics, finance, physics, and more. Here are two examples:

Stock prices: The stock market is a classic example of a stochastic process. The price of a particular stock is influenced by a wide range of factors, including economic conditions, company performance, and investor sentiment. These factors are often difficult to predict with complete accuracy, leading to uncertainty about the future price of a stock. As a result, stock prices can be highly unpredictable and subject to significant randomness.

Brownian motion: Brownian motion is a type of random motion that was first observed by botanist Robert Brown in 1827. He noticed that small particles suspended in a liquid seemed to be moving randomly and unpredictably. This motion is now known to be caused by the constant bombardment of the particles by molecules in the liquid. Brownian motion is an example of a stochastic process, as the motion of the particles is not completely determined and is subject to some degree of randomness.

These are just a couple of examples of stochastic processes, but there are many others as well. In general, a stochastic process is any process in which the outcome is not completely determined and is subject to some degree of randomness. This can be due to a wide range of factors, including external influences, inherent uncertainty, and more. Understanding and modeling stochastic processes is an important task in many fields, as it can help us to better understand and predict the behavior of systems that are subject to randomness and uncertainty.