Article
Full entry |
PDF
(1.9 MB)
Feedback
PDF
(1.9 MB)
Feedback
Keywords:
linear transformations of a Wiener process; Brownian bridge; Ornstein-Uhlenbeck process
linear transformations of a Wiener process; Brownian bridge; Ornstein-Uhlenbeck process
Summary:
The paper presents a discussion on linear transformations of a Wiener process. The considered processes are collections of stochastic integrals of non-random functions w.r.t. Wiener process. We are interested in conditions under which the transformed process is a Wiener process, a Brownian bridge or an Ornstein –Uhlenbeck process.
References:
[1] Billingsley P.: Convergence of Probability Measures. Wiley, New York 1968 MR 0233396 | Zbl 0944.60003
[2] Brockwell P. J., Davis R. A.: Time Series – Theory and Methods. Springer, New York 1987 MR 0868859 | Zbl 1169.62074
[3] Hoffmann–Jørgensen J.: Probability with a View Towards to Statistics I. Chapman and Hall, New York 1994
[4] Hoffmann–Jørgensen J.: Probability with a View Towards to Statistics II. Chapman and Hall, New York 1994
[5] Kallenberg O.: Foundation of Modern Probability. Springer, Berlin 1997 MR 1464694
[6] Revuz D., Yor M.: Continuous Martingales and Brownian Motion. Springer, Berlin 1991 MR 1083357 | Zbl 1087.60040
Search
Partner of
