A Gaussian stochastic process (a continuous-time stochastic process) that has independent increments and a vanishing mean, and it features an increment of the process during any specific time period that has a variance proportional to the time period. It is by nature a Markov process and a martingale process. As a Markov process, the probability distribution of all future values of the process depends solely on the current value.

The changes in the distribution follow a normal distribution pattern with variance that increases linearly with the time period. A Wiener process projects a limit of random walks where during every time interval a variable follows on a linear trajectory, maintaining a fixed distance on both sides with equal probability.

A Wiener process is also known as a standard Brownian motion.