Nonlinear filtering in spatio–temporal doubly stochastic point processes driven by OU processes

Michaela Prokešová; Viktor Beneš

Kybernetika (2006)

  • Volume: 42, Issue: 5, page 539-556
  • ISSN: 0023-5954

Abstract

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Doubly stochastic point processes driven by non-Gaussian Ornstein–Uhlenbeck type processes are studied. The problem of nonlinear filtering is investigated. For temporal point processes the characteristic form for the differential generator of the driving process is used to obtain a stochastic differential equation for the conditional distribution. The main result in the spatio-temporal case leads to the filtering equation for the conditional mean.

How to cite

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Prokešová, Michaela, and Beneš, Viktor. "Nonlinear filtering in spatio–temporal doubly stochastic point processes driven by OU processes." Kybernetika 42.5 (2006): 539-556. <http://eudml.org/doc/33823>.

@article{Prokešová2006,
abstract = {Doubly stochastic point processes driven by non-Gaussian Ornstein–Uhlenbeck type processes are studied. The problem of nonlinear filtering is investigated. For temporal point processes the characteristic form for the differential generator of the driving process is used to obtain a stochastic differential equation for the conditional distribution. The main result in the spatio-temporal case leads to the filtering equation for the conditional mean.},
author = {Prokešová, Michaela, Beneš, Viktor},
journal = {Kybernetika},
keywords = {Cox process; filtering; Ornstein–Uhlenbeck process; Cox process; filtering; Ornstein-Uhlenbeck process},
language = {eng},
number = {5},
pages = {539-556},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Nonlinear filtering in spatio–temporal doubly stochastic point processes driven by OU processes},
url = {http://eudml.org/doc/33823},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Prokešová, Michaela
AU - Beneš, Viktor
TI - Nonlinear filtering in spatio–temporal doubly stochastic point processes driven by OU processes
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 5
SP - 539
EP - 556
AB - Doubly stochastic point processes driven by non-Gaussian Ornstein–Uhlenbeck type processes are studied. The problem of nonlinear filtering is investigated. For temporal point processes the characteristic form for the differential generator of the driving process is used to obtain a stochastic differential equation for the conditional distribution. The main result in the spatio-temporal case leads to the filtering equation for the conditional mean.
LA - eng
KW - Cox process; filtering; Ornstein–Uhlenbeck process; Cox process; filtering; Ornstein-Uhlenbeck process
UR - http://eudml.org/doc/33823
ER -

References

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  2. Beneš V., Prokešová M., Nonlinear filtration in doubly stochastic point processes, In: Proc. 4th International Conference Aplimat 2005 (M. Kováčová, ed.), FME, Slovak Technical University, Bratislava 2005, pp. 415–420 
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  13. Sato K., Basic results on Lévy processes, In: Lévy Processes – Theory and Applications (O. Barndorff-Nielsen, T. Mikosch, and S. Resnick, eds.), Birkäuser, Boston 2001 Zbl0974.60036MR1833689
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