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Wiener process
In mathematics, the Wiener process, so named in honor of Norbert Wiener, is a continuous-time Gaussian stochastic process with independent increments used in modelling Brownian motion and some random phenomena observed in finance. It is one of the most well-known Lévy processes. For each positive number t, denote the value of the process at time t by Wt. Then the process is characterized by the following two conditions:
- If 0 < s < t, then
- ("N(μ, σ2)" denotes the normal distribution with expected value μ and variance σ2.)
- If 0 ≤ s ≤ t ≤ u ≤ v, (i.e., the two intervals [s, t] and [u, v] do not overlap) then
The paths are almost surely continuous. The Wiener measure is the probability law on the space of continuous functions g, with g(0) = 0, induced by the Wiener process. An integral based on Wiener measure may be called a Wiener integral.
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details