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.
Wiener Process
See also
Ito's Lemma, Random Walk, Wiener MeasureExplore with Wolfram|Alpha
References
Finch, S. "Ornstein-Uhlenbeck Process." May 15, 2004. http://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.Referenced on Wolfram|Alpha
Wiener ProcessCite this as:
Weisstein, Eric W. "Wiener Process." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WienerProcess.html