Wiener Process

A continuous-time stochastic process  for  with  and such that the increment  is Gaussian with mean 0 and variance  for any , and increments for nonoverlapping time intervals are independent. Brownian motion (i.e., random walk with random step sizes) is the most common example of a Wiener process.

REFERENCES:

Finch, S. "Ornstein-Uhlenbeck Process." May 15, 2004. https://algo.inria.fr/csolve/ou.pdf.

Karatsas, I. and Shreve, S. Brownian Motion and Stochastic Calculus, 2nd ed. New York: Springer-Verlag, 1997.

Papoulis, A. "Wiener-Lévy Process." §15-3 in Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 292-293, 1984.