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Details for article 2 of 9 found articles
| Title: |
A generalized ornstein-uhlenbeck process |
| Author: |
Wittig, Timothy A. |
| Appeared in: |
Communications in statistics |
| Paging: | Volume 13 (1984) nr. 1 pages 29-43 |
| Year: |
1984 |
| Contents: |
We construct a generalized Ornstein-Uhlenbeck velocity process as a Gaussian process with a prescribed continuous covariance on [image omitted] (Hσ Sobolev space). It is shown that this can be realized in [image omitted] and solves a martingale problem analogous to the work in [7]. In fact for σ = 0 this gives their result. This process satisfies, in the weak sense, an operator-valued analog of the Langevin equation in [ll]. We give an example of Einstein's conditions ((A.3), (A.4)) and under these derive the Wiener process as a limit of displacement processes associated with these velocity processes. It is shown that this gives a precise generalization of the classical work of Ornstein, Uhlenbeck and Wang [11]. |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 2 of 9 found articles
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