Filtering with Marked Point Process Observations via Poisson Chaos Expansion
Abstract
We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical scheme based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.
- Authors:
- Concordia University, Department of Mathematics and Statistics (Canada)
- University of Missouri at Kansas City, Department of Mathematics and Statistics (United States)
- Publication Date:
- OSTI Identifier:
- 22156272
- Resource Type:
- Journal Article
- Journal Name:
- Applied Mathematics and Optimization
- Additional Journal Information:
- Journal Volume: 67; Journal Issue: 3; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; CALCULATION METHODS; CHAOS THEORY; MATHEMATICAL SOLUTIONS; POISSON EQUATION; STOCHASTIC PROCESSES
Citation Formats
Sun Wei, E-mail: wsun@mathstat.concordia.ca, Zeng Yong, E-mail: zengy@umkc.edu, and Zhang Shu, E-mail: zhangshuisme@hotmail.com. Filtering with Marked Point Process Observations via Poisson Chaos Expansion. United States: N. p., 2013.
Web. doi:10.1007/S00245-012-9189-6.
Sun Wei, E-mail: wsun@mathstat.concordia.ca, Zeng Yong, E-mail: zengy@umkc.edu, & Zhang Shu, E-mail: zhangshuisme@hotmail.com. Filtering with Marked Point Process Observations via Poisson Chaos Expansion. United States. https://doi.org/10.1007/S00245-012-9189-6
Sun Wei, E-mail: wsun@mathstat.concordia.ca, Zeng Yong, E-mail: zengy@umkc.edu, and Zhang Shu, E-mail: zhangshuisme@hotmail.com. 2013.
"Filtering with Marked Point Process Observations via Poisson Chaos Expansion". United States. https://doi.org/10.1007/S00245-012-9189-6.
@article{osti_22156272,
title = {Filtering with Marked Point Process Observations via Poisson Chaos Expansion},
author = {Sun Wei, E-mail: wsun@mathstat.concordia.ca and Zeng Yong, E-mail: zengy@umkc.edu and Zhang Shu, E-mail: zhangshuisme@hotmail.com},
abstractNote = {We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical scheme based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.},
doi = {10.1007/S00245-012-9189-6},
url = {https://www.osti.gov/biblio/22156272},
journal = {Applied Mathematics and Optimization},
issn = {0095-4616},
number = 3,
volume = 67,
place = {United States},
year = {Sat Jun 15 00:00:00 EDT 2013},
month = {Sat Jun 15 00:00:00 EDT 2013}
}