Stochastic Processes

A stochastic process is a random function; or more precisely, an indexed family of random variables.

"stochastic adjective randomly determined; having a random probability distribution or pattern that may be analysed statistically but may not be predicted precisely."
The New Oxford Dictionay of English, 1998

"stochastic process, n. a process that can be described by a RANDOM VARIABLE (stochastic variable) that depends on some parameter, which may be discrete or continuous, but is often taken to represent time; precisely, an indexed family of random variables, called states, on a probability space. A stochastic process is finite if the index familiy is countable and each state is a step function. A MARKOV CHAIN is a discrete-parameter stochastic process in which future probabilities are completely determined by the present state."
Borowski and Borwein, 1989

"In the mathematics of probability, a stochastic process is a function. In the most common applications, the domain over which the function is defined is a time interval (a stochastic process of this kind is called a time series in applications) or a region of space (a stochastic process being called a random field)."
Wikipedia (2006)