Linear transformations of Wiener process that born Wiener process, Brownian bridge or Ornstein-Uhlenbeck process

Petr Lachout

Kybernetika (2001)

  • Volume: 37, Issue: 6, page [647]-667
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Lachout, Petr. "Linear transformations of Wiener process that born Wiener process, Brownian bridge or Ornstein-Uhlenbeck process." Kybernetika 37.6 (2001): [647]-667. <http://eudml.org/doc/33557>.

@article{Lachout2001,
abstract = {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.},
author = {Lachout, Petr},
journal = {Kybernetika},
keywords = {linear transformations of a Wiener process; Brownian bridge; Ornstein-Uhlenbeck process; linear transformations of a Wiener process; Brownian bridge; Ornstein-Uhlenbeck process},
language = {eng},
number = {6},
pages = {[647]-667},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Linear transformations of Wiener process that born Wiener process, Brownian bridge or Ornstein-Uhlenbeck process},
url = {http://eudml.org/doc/33557},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Lachout, Petr
TI - Linear transformations of Wiener process that born Wiener process, Brownian bridge or Ornstein-Uhlenbeck process
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 6
SP - [647]
EP - 667
AB - 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.
LA - eng
KW - linear transformations of a Wiener process; Brownian bridge; Ornstein-Uhlenbeck process; linear transformations of a Wiener process; Brownian bridge; Ornstein-Uhlenbeck process
UR - http://eudml.org/doc/33557
ER -

References

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  1. Billingsley P., Convergence of Probability Measures, Wiley, New York 1968 Zbl0944.60003MR0233396
  2. Brockwell P. J., Davis R. A., Time Series – Theory and Methods, Springer, New York 1987 Zbl1169.62074MR0868859
  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 MR1464694
  6. Revuz D., Yor M., Continuous Martingales and Brownian Motion, Springer, Berlin 1991 Zbl1087.60040MR1083357

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