| Title:
|
Linear transformations of Wiener process that born Wiener process, Brownian bridge or Ornstein-Uhlenbeck process (English) |
| Author:
|
Lachout, Petr |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
37 |
| Issue:
|
6 |
| Year:
|
2001 |
| Pages:
|
[647]-667 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
linear transformations of a Wiener process |
| Keyword:
|
Brownian bridge |
| Keyword:
|
Ornstein-Uhlenbeck process |
| MSC:
|
60G15 |
| MSC:
|
60J65 |
| idZBL:
|
Zbl 1265.60082 |
| idMR:
|
MR1936993 |
| . |
| Date available:
|
2009-09-24T19:42:32Z |
| Last updated:
|
2015-03-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135434 |
| . |
| Reference:
|
[1] Billingsley P.: Convergence of Probability Measures.Wiley, New York 1968 Zbl 0944.60003, MR 0233396 |
| Reference:
|
[2] Brockwell P. J., Davis R. A.: Time Series – Theory and Methods.Springer, New York 1987 Zbl 1169.62074, MR 0868859 |
| Reference:
|
[3] Hoffmann–Jørgensen J.: Probability with a View Towards to Statistics I.Chapman and Hall, New York 1994 |
| Reference:
|
[4] Hoffmann–Jørgensen J.: Probability with a View Towards to Statistics II.Chapman and Hall, New York 1994 |
| Reference:
|
[5] Kallenberg O.: Foundation of Modern Probability.Springer, Berlin 1997 MR 1464694 |
| Reference:
|
[6] Revuz D., Yor M.: Continuous Martingales and Brownian Motion.Springer, Berlin 1991 Zbl 1087.60040, MR 1083357 |
| . |
