Wiener process

The Wiener process, so named in honor of Norbert Wiener, is a continuous-time Gaussian stochastic process used in modelling Brownian motion and some random phenomena observed in financial markets. For each positive number t, denote the value of the process at time t by W_t. Then the process is characterized by the following conditions: If 0 < s < t, then

("N(μ, σ)" denotes the normal distribution with expected value μ and variance σ².)

If 0 < s < t < u < v, then

are independent random variables.