an indexed collection of random variables , each of which is defined on the same probability space "W" and takes values on the same codomain D (often the reals R )

an ordered collection of random variables

a probabilistic model of a system that evolves randomly in time and space

a random process evolving with time

a stochastic process is one that can be described by the evolution of some random variable over some parameter such as time. One example is geometric Brownian motion, which is commonly used to describe the movements of asset prices.

A process, the outcome of which cannot be predicted exactly from knowledge of initial conditions.

A process of change governed by probabilities at each step.

Any process in which there is a random element. Stochastic processes are important in non-equilibrium statistical mechanics and disordered solids. In a time-dependent stochastic process, a variable that changes with time does so in such a way that there is no correlation between different time intervals.

A system that evolves in time according to probabilistic equations, that is, the behavior of the system is determined by one or more time-dependent random variables.

A random process which evolves over time.

In the mathematics of probability, a stochastic process or random process is a process that can be described by a probability distribution. The two most common types of stochastic processes are the time series, which has a time interval domain, and the random field, which has a domain over a region of space.